Speaking before New York's exhibition game at the Washington Nationals on Friday, Teixeira said his goal is to rejoin the Yankees as soon as May 1.
He will start the season on the disabled list because of a partially torn tendon sheath in his right wrist.
"Like a pitcher coming back from Tommy John (elbow surgery), throwing through pain isn't a good idea," Teixeira said. "So I just have to be smart with it."
He has been taking grounders since last weekend and practice swings with one hand on his bat.
"My plan is to not skip a beat when I come back," Teixeira said.
General manager Brian Cashman said "it's way too early" to know much about how Teixeira's wrist is healing.
"But I know one thing: He's busting his tail," Cashman said. "He's doing leg stuff, he's doing all these different stuff, so every aspect of his body other than the wrist can be better."
Cashman also said shortstop Derek Jeter, still recovering from left ankle surgery in October, needs some time for "rest and treatment."
"I know he isn't supposed to do anything until Monday at the earliest," Cashman said. "Get the soreness out and back off. Take the two steps back so he can take a giant step forward."
Like Teixeira, Jeter will begin the season on the DL. April 6 is the earliest Jeter could be activated.