The team confirmed in a statement Sunday that the 25-year-old woman, who is still missing at sea, is Gainey's daughter.
Gainey was with his three other children, Anna, Colleen and Steve, the statement from team president Pierre Boivin and communications vice-president Donald Beauchamp said.
"In respecting the privacy of Mr. Gainey and his family, the Canadiens will not issue any further comment at this time," the statement read. "For the time being, Mr. Pierre Gauthier will manage the responsibilities of Mr. Gainey with the Canadiens."
Craig Button, a pro scout for the Toronto Maple Leafs who worked with Gainey when the former Canadiens captain was GM in Minnesota and Dallas, said the team is in good hands.
Gauthier was president and GM in Anaheim from 1998 to 2002 and was GM in Ottawa from 1995 to 1998.
"He knows the role and he's comfortable in it," Button said. "He can certainly fulfill the obligations of that position in Bob's absence."
Button was shaken by the news and said "you pray for them to find the strength to get through this together."
Gainey learned that the missing woman was his daughter on Saturday. Gauthier attended the Canadiens 3-2 shootout loss to Buffalo on Saturday night at the Bell Centre.
Laura, the third of Gainey's four children, was on a tall ship, the Picton Castle, headed to Granada when she was swept overboard by a large wave at about 9:30 p.m. on Friday. Rescuers are searching for her off the U.S. coast.
The Canadiens players and coaches had a day off practice Sunday and were not available for comment.
Gainey lost his wife Cathy to a five-year battle with brain cancer in 1995, when she was 39.
Gainey, who turns 53 on Wednesday, is a former Canadiens captain who won five Stanley Cups from 1973 to 1989. He joined the Minnesota North Stars, now the Dallas Stars, as head coach in 1990 and added the GM title in 1992. His Stars won a Stanley Cup in 1999.
Steve Gainey, 27, was drafted in the third round by Dallas in 1997, but spent most of his career in the minors. He signed with the Phoenix Coyotes in 2005 and played 20 games last season. He is not playing this season.
In his NHL career, he has no goals and two assists in 33 games.