New York general manager Jeff Gorton said the accident didn't impact his decision-making in advance of the 2020 NHL Trade Deadline on Monday.
The Rangers agreed to terms with forward Chris Kreider on a seven-year, $45.5 million contract ($6.5 million average annual value) that will keep him from becoming an unrestricted free agent.
They also traded defenseman Brady Skjei to the Carolina Hurricanes for a first-round pick in the 2020 NHL Draft.
"It's an unfortunate incident that happened," Gorton said. "We're thankful that the accident wasn't worse and that these guys are going to be OK rather soon."
Georgiev is expected to start against the New York Islanders at Nassau Coliseum on Tuesday (7 p.m. ET; ESPN+, MSG+ 2, MSG, NHL.TV). But Shesterkin's injury means Lundqvist could get some playing time in the coming weeks that he might not have otherwise.
Lundqvist, whose 459 wins are sixth in NHL history, has gone 10 straight games without a start. He has started three of the Rangers' 20 games since they recalled Shesterkin from Hartford of the American Hockey League on Jan. 6.
"Moving forward here, practice, playing, my obligation, my job is to come here and give it my all, and that what I've been trying to do over the last few weeks, just be ready when I get the opportunity to play," said Lundqvist, who has one season remaining on a seven-year contract. "But if I'm not playing, try to be as supportive as possible to the guys that are playing. I think that's what you should do. It's been a very unique situation, obviously, but now whatever happens here down the stretch, you've just got to come here with positive energy and try to help the team in any way you can."