Kreider left a 1-0 shootout win against the Washington Capitals on Wednesday with 22 seconds remaining in the first period.
Rangers coach Alain Vigneault said Thursday that Kreider felt swelling in his arm before the game but was cleared to play after being examined by doctors. He played seven shifts totaling 5:04 and had two shots on goal, and after the first period, the swelling had increased and Kreider was sent to the hospital, where testing discovered the blood clot.
"In between the first and second [the swelling] got to a point where this was out of the ordinary," Vigneault said. "So [doctors] sent him to the hospital and found it out."
Kreider is tied for fourth on the Rangers with 22 points (11 goals, 11 assists) in 37 games.
The Rangers recalled forward Vinni Lettieri from Hartford of the American Hockey League. The 22-year-old has 21 points (12 goals, nine assists) in 31 games.
Vigneault said he liked Lettieri's skill set and right-handed shot, and he'll get a chance to play.
"The combination of him being a righty and a righty that likes to shoot the puck, we don't have a lot of that on our team," Vigneault said. "He's been doing that in Hartford. I've tried some other guys and I want to try Vinni."
The Rangers play at the Detroit Red Wings on Friday (7:30 p.m. ET; FS-D, MSG, NHL.TV) and then play the Buffalo Sabres in the 2018 Bridgestone NHL Winter Classic at Citi Field in New York on Monday (1 p.m. ET; NBC, SN, TVA Sports, NHL.TV).