The 33-year-old suffered the injury in the early minutes of the second half of his side's 3-0 home win against Fortuna Dusseldorf in the Bundesliga on Friday following a collision with Andreas Lambertz.
"I have broken my hand," Gomes told reporters. "But I will return stronger than ever."
Gomes, who joined Hoffenheim on loan from Tottenham Hotspur in January, was replaced by Koen Casteels, who has since been confirmed by club coach Markus Gisdol as the team's number one goalkeeper for the remainder of the season.
Hoffenheim are currently second from bottom in the Bundesliga with 23 points from 28 matches.