The team also denied a published report in the New York Daily News -- which first reported Avery's hospitalization -- that the forward had been taken to a Manhattan hospital while unconscious and in cardiac arrest.
The Rangers said Avery was admitted to St. Vincent's Medical Center following a CT scan and is expected to make a full recovery. Avery walked into the medical facility with team doctor Andrew Feldman, and the two took a car to the hospital, not an emergency vehicle, the team said.
Michael Fagan, spokesman for St. Vincent's Medical Center, said Avery is in "stable" condition.
Tuesday night, the Rangers lost 5-3 in the Stanley Cup playoffs against the Pittsburgh Penguins at Madison Square Garden. The Penguins took a 3-0 series lead with the win.
Avery suffered the injury as the result of a hit during the game, spokesman John Rosasco told reporters during the team's morning workout.
"He walked into the hospital," Rosasco said. "He was never in a life-threatening situation."
Avery's mother Marlene told the Toronto Sun that the injury occurred in the first period as the result of a collision with a Penguins defenseman and that her son played the remainder of the game in a great deal of pain. She said his spleen had not ruptured, but that he had suffered internal bleeding.
Avery played 14 minutes and 34 seconds of Game 3, taking 19 shifts on the ice. He finished the game before going to the hospital, according to the team. He has seven points in eight playoff games this spring.
"We're definitely going to miss him," forward Ryan Callahan said after practice Wednesday. "He's a real big part of the team. He's come up with some real big points, scored big goals and obviously gets under the other team's skin.
"It's a tough loss to lose him, but we've got a lot of guys in here. Guys have to step up, and we have to concentrate on the next game."
Avery, known for irritating opponents' skin with a chippy style of play, became a lightning rod for controversy during the first round when he tried to disrupt New Jersey Devils netminder Martin Brodeur by waving his arms and stick in the netminder's face. The unorthodox method of screening prompted the NHL to impose a new rule that warned similar actions by players would result in a penalty.
The spleen is an organ about the size of a fist on the left side of the body, behind the stomach. It helps the body fight infection and filters the blood. A person can live without a spleen, although he loses some of his ability to fight infections.
In his NHL time with the Detroit Red Wings, the Kings and the Rangers, Avery has elevated a knack of riling people into an art form. His targets find themselves mouthing off, or worse, getting so angered that they draw a penalty.
"On the ice, things always happen," Penguins captain Sidney Crosby said. "It's emotional and intense. Guys are not the best of friends on the ice, but you never want to see someone's health in jeopardy. I think we all wish him the best.
"He's a guy who brings a lot of emotion to his team. I think we are a good example, we learned from when we lost some guys that other guys step up. When you lose guys you push harder to be better. So I don't think any of us will take that for granted."
Avery has also had an ongoing feud with 41-year-old Penguins forward Gary Roberts, who has yet to play in this series. Despite his 21 seasons of NHL experience, Roberts lost his cool during a November game and took a 4-minute high-sticking penalty against Avery that led to a goal in a Rangers victory.
"A guy like that, they take it a little bit more of an insult after you disrespect them and all they've done for the game and how great they are," Avery said then of Roberts.
Roberts called Avery "an idiot" after his antics with Brodeur, but took a softer tone when told of the injury.
"There's hockey and then there is life and your health. You don't wish that on anybody," Roberts said. "I don't know Sean personally away from the rink. Obviously, we've had our comments throughout the media, but truthfully when it comes to this kind of stuff you just hope that he makes a full recovery."
Scott Burnside is a senior writer for ESPN.com. The Associated Press contributed to this report.