The England No. 1 went for the ball against Cameron Jerome in the first half, and his face met Jerome's knee.
Jerome, unable to continue, substituted off in the 35th minute.
Despite his eye closing up, Hart stayed on for Manuel Pellegrini's men, and Man City ultimately prevailed 1-0.
He has only recently regained the gloves from rival keeper Costel Pantilimon at the Etihad Stadium.