Davis has a torn labrum in his left shoulder and a left knee injury, the Pelicans announced. He will undergo procedures to correct both.
Davis' exit after 61 games played this season puts his chances of being voted onto one of three end-of-season All-NBA teams -- and thus earning an estimated $24 million extra for the maximum extension he signed with the Pelicans the past offseason -- in jeopardy.
Gentry said he didn't know if the surgery would impact Davis' status for the 2016 Rio Olympics, but he said, "If I was a betting man, probably so, yeah."
"He's disappointed. He's very disappointed," Gentry said. "You know good and well that he loves playing and wants to be good. He feels a huge obligation to try to make this team better, try to get them back to where they were last year -- making the playoffs and stuff like that."
Pelicans guard Jrue Holiday said he hopes Davis' rehabilitation doesn't derail his Olympic prospects.
"I feel like this time he would have more of a prominent role on that team; It would be awesome to watch him play'' for Team USA this summer, Holiday said. "But obviously he's going to make the right decision for himself.''
Davis, 23, is now the fifth New Orleans player -- and fourth projected opening-day starter -- sidelined for the rest of the season. Quincy Pondexter (left knee) is missing every game in 2015-16, and Tyreke Evans (right knee), Eric Gordon (right ring finger) and Bryce Dejean-Jones (right wrist) have been shut down. Ryan Anderson will miss his third game of the season because of a groin strain and Norris Cole (lower back) will miss his seventh straight game when the Pelicans host the Clippers on Sunday.
Pelicans players have missed a combined 229 games because of injuries this season. Including illnesses and personal absences, the players have missed 235 games. Their 34 starting lineup combinations are the most in the NBA.
"It's hard, especially when your franchise leader goes down," said Kendrick Perkins, who has served as a mentor to Davis this season. "At the end of the day, nobody gonna feel sorry for [us]. You gotta go out there and compete. He had some nicks and bruises that he needed to get done, some real injuries he needed to get done. It's the perfect time. We not making the playoffs. It's unfortunate for him that he probably won't play in the Olympics this summer, but the guys in the locker room now, we just got to pull together and close the season out and get wins."
Davis finishes the season with averages of 24.3 points, 10.3 rebounds and 2.0 blocks per game. His 25.21 player efficiency rating ranks seventh in the NBA, and his real plus-minus of plus-2.74 ranks 36th.
The 2012 No. 1 overall pick has missed 14 or more games in each of his three previous seasons.
"This is the most frustrating season I've ever been through,'' said Gentry, who is in his first year with New Orleans after serving as a top assistant with Golden State during its 2014-15 championship season. "When I left Golden State to come here, I thought it was the best job available.''
"We've got to plan for the future, and I think we've got a bright future here,'' Gentry said. "We have arguably the best player in the NBA. We have some good pieces and we're going to add some pieces'' in the offseason.
Information from The Associated Press was used in this report.