The former England international Frank Lampard sustained the injury in their 2-2 MLS draw with Dallas on Sunday.
Lampard, 38, has scored 12 goals and added an assist in 18 MLS regular season appearances this season.
New York City are third in the Eastern Conference with four games of the regular season remaining.

Patrick Vieira’s men are level on points with second-placed New York Red Bulls and take on Chicago Fire at Yankee Stadium on Saturday.

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