The American defender, who conceded a penalty in the match to allow City's Erling Haaland to score early on, fell awkwardly after slipping and went off with his arm in a makeshift sling.
"It looked clear Tim Ream will not play for us this season, broken his arm," Fulham manager Marco Silva said.
Tenth-placed Fulham also had midfielder Andreas Pereira carried off on a stretcher in the second half, adding to their problems with forward Aleksandar Mitrovic suspended and midfielder Willian also out.
"This is clearly the worst thing of the afternoon. The result, everything that's happened is not important when after the Mitrovic situation and Willian out as well, two more key players are out with serious injuries," Silva said.
"Let's hope Andreas is not so serious, but it looks serious. They're both in hospital and the medical staff will assess them."
