The 35-year-old left the field during the first half of Sunday's 2-1 home defeat against Manchester City with his arm in a makeshift sling after falling awkwardly following a tussle with Julian Alvarez.
Ream went to the hospital along with Andreas Periera, who was stretchered off in the second half after a challenge with Manuel Akanji.
"A tough afternoon for us because we lost another two players in Tim Ream and Andreas Periera," Silva said. "Both look like really serious injuries so it is a tough moment but we have to keep going, more games to play."
Asked whether both players would be out for the season, Silva told BeIn Sports: "Tim Ream for sure, unfortunately for us. He has broken his arm. Let's see on Andreas, I hope it is not so serious, but I have to wait for more [information]."
Erling Haaland and Alvarez scored City's goals either side of Carlos Vinicius' 15th-minute equaliser as Pep Guardiola's side returned to the top of the Premier League for the first time since Feb. 15. Fulham sit in 10th place with 45 points from 33 games.
Ream's involvement with the USMNT's busy upcoming summer is now unclear, but the veteran played a key role during their run to the round of 16 at the World Cup last December. The Americans will compete in the CONCACAF Nations League final in June and then take part in the Gold Cup beginning in July.