Spaniard Silva received treatment for nearly 10 minutes and was carried off on a stretcher after being hit on the head by the elbow of West Ham midfielder Cheikhou Kouyate.
"At this moment he (David Silva) is in hospital and they are checking if he has a broken bone in his cheek," manager Manuel Pellegrini told reporters.
"I always think that a player doesn’t want to damage another player, the ref decided it was unintentional and I also think that."
After losing back-to-back league games, victory for fourth-placed City eased the pressure on Pellegrini and the champions now have 64 points, one behind Manchester United who lost 1-0 at Chelsea on Saturday.
"It was important to win because we come from two defeats," Pellegrini said.
"We must continue working altogether and it is very important to finish as near to the top of the table as possible."
(Reporting by Michael Hann, editing by Ed Osmond)
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