Gallinari was injured in the third quarter, and X-rays revealed the fracture to his non-shooting hand. He did not return to the game.
"I don't know how long it's going to be," Gallinari said, according to the Denver Post. "It's not going to be short. It's a fracture. The doctor told me the fracture takes four weeks to heal. Hopefully I can put something on and play sooner than that."
Gallinari missed 13 games with a severely sprained ankle suffered against Houston on Feb. 6. He returned to the lineup March 5 and had started to regain his rhythm.
Gallinari leads the Nuggets in scoring at 15.6 points a game and is averaging 4.6 rebounds.
Nuggets guard Andre Miller also bruised his right shoulder in Monday's game and didn't return.
"I'm pretty certain Gallo won't play Wednesday and we'll find out more (Tuesday)," Nuggets coach George Karl said, according to the newspaper. "My gut says Andre will play."
Information from The Associated Press was used in this report.