Adenhart, 22, from Silver Spring, Maryland, died at UC Irvine Medical Center, according to spokesman John Murray.
"The Angels family has suffered a tremendous loss today," Tony Reagins, the team's general manager, said in a written statement. "We are deeply saddened and shocked by this tragic loss. Our thoughts and prayers go out to Nick's family, friends, loved ones and fans."
One person was arrested in connection with the three-vehicle accident occurred about 12:23 a.m. Thursday in Fullerton, south of Los Angeles. Witnesses say a red minivan ran a red light and struck two vehicles at a Fullerton intersection, police Lt. Craig Brower told CNN.
One of the vehicles, a gray Mitsubishi, slammed into a power pole, Brower said. Two of its passengers were dead at the scene, he said. The other two were transported to UC Irvine Medical Center.
Murray said Adenhart underwent surgery and died at the hospital, but did not know if he died during or after the procedure. Brower said the remaining passenger was in critical condition.
The Angels said the two dead at the scene included the female driver of the Mitsubishi and another male. No other members of the Angels organization were involved, the team said.
Adenhart reportedly was "in bad condition at the scene," team spokesman Tim Mead told reporters, and there wasn't much that could be done for him at the hospital. He died "mid- to late morning," Mead said.
A passenger in the minivan was taken to a hospital with minor injuries, Brower said. The third vehicle sustained minor damage, and its driver was unhurt, he said. Police did not identify any of the dead.
The minivan's driver fled the scene and was later arrested, Brower said. Andrew Thomas Gallo, 22, of Riverside will face charges of manslaughter, felony driving under the influence and hit-and-run, he said.
Footage from the scene showed the minivan with a smashed front end and the Mitsubishi, which was heavily damaged. Debris littered the intersection where the crash took place, and it was cordoned off with yellow police tape.
The Angels' game Thursday night with the Oakland A's was postponed at the direction of Bud Selig, commissioner of Major League Baseball. No information was released as to when the game would be played.
"Major League Baseball is in mourning today upon the news of this tragedy that has taken Angels pitcher Nick Adenhart and two others," Selig said in a statement. "Nick was just 22 years of age, with a wonderful life and career ahead of him. On behalf of Major League Baseball, I extend my sincere sympathy to the families and friends of all three victims and to the entire Angels' organization. I send my deepest condolences to Nick's parents, Jim and Janet. The hearts of everyone in baseball are with them at this most difficult time."
The Angels quoted Adenhart's family in the team statement, saying they "expresses sincere gratitude for all the help the Angels have provided.
"He lived his dream and was blessed to be part of an organization comprised of such warm, caring and compassionate people," Adenhart's parents said in the Angels statement. "The Angels were his extended family. Thanks to all of Nick's loyal supporters and fans throughout his career. He will always be in everyone's hearts forever."
Funeral and memorial arrangements were pending, the team said.
MLBPA Executive Director Donald Fehr issued the following statement.: "We were shaken and deeply saddened when we learned about the terrible accident that claimed the lives of Nick Adenhart and others. Just hours before the accident, Nick demonstrated his passion for baseball and his prospects for a very bright future when he pitched six scoreless innings for the Angels. Our thoughts and prayers go out to Nick's family, his teammates, the Angels organization and his many friends and fans; it is very painful to lose a son, a teammate and a friend under these circumstances, and we also extend our deepest condolences to the families and friends of the other victims of the crash."
Adenhart pitched in a game against the Oakland A's Wednesday night in Anaheim, California, making what was characterized as a "brilliant effort" despite the Angels' 6-4 loss, according to Major League Baseball's Web site, MLB.com.
In his fourth major league start, Adenhart pitched a scoreless six innings, allowing seven hits, three walks and five strikeouts.
"I thought he pitched a terrific game," manager Mike Scioscia told MLB.com after the game and before the crash took place. "He gave us a chance to win. He has better tools out there now. He pitched ahead a lot and was able to get back in counts and put guys away."
"It felt good to work out of some jams early," Adenhart told MLB.com. "My curveball was really working for me, and then my change came on later when I felt I needed it."
Jim Adenhart had flown out from Baltimore, Maryland, and was at Wednesday night's game to watch his son's start, his first of the season, Mead said. He remained in California Thursday, and Janet Adenhart was expected to fly out later in the day.
The Angels drafted Adenhart in the 14th round of the June 2004 draft, according to the team statement. He was in his fifth professional season and made the Angels Opening Day Roster for the first time.
"Adenhart earned his spot in the Angels rotation via a spring training in which he recorded a 3-0 record and a 3.12 ERA over the course of six starts," the team statement said. "During that span, he struck out 18 while allowing only five base on balls."
Adenhart made his major league debut May 1, 2008, against Oakland, the team said. At the time, he was the youngest active-roster pitcher in the majors.
Adenhart was a 2004 graduate of Williamsport High School in Williamsport, Maryland. His baseball coach there, Rod Steiner, told CNN affiliate WHAG, "After watching last night, as well as he pitched ... things seemed to be going so smooth. This is the last thing that you ever imagine."
He remembered Adenhart as a hard worker who knew he wanted to be a major-league pitcher while still in high school, and worked hard to achieve that goal, despite a setback when he had to undergo shoulder surgery.
He said area residents who didn't even know Adenhart followed his career and cheered him on. "He touched a lot of lives."
Adenhart was a member of the 2006 Olympic Qualifying Team that traveled to Cuba and qualified the United States for the Beijing 2008 Olympic Games. He started one game for Team USA, earning a no-decision and striking out six batters in an 8-7 win over Brazil.
"You're never prepared for this kind of news," USA Baseball Executive CEO Paul Seiler said. "We, like the entire the baseball community, mourn the loss of someone so young who was in the prime of his life. Our thoughts go out to his family, his teammates and the entire Angels organization."
Davey Johnson, who managed the 2006 Olympic Qualifying Team, fondly remembered his time with Adenhart.
"One of the highlights of managing for USA Baseball is the opportunity to work with bright, young players who are eager to learn the game. Nick embodied all of those attributes. He was a joy to manage in Cuba and was a key contributor to our success there. This is such a tragedy -- his career was just getting started."
-- CNN's Rosalina Nieves and Irving Last contributed to this report.