The Hammers were set to host City on Saturday but after four players or staff members at the Manchester club returned positive tests the Football Association have called the match off at City's request.
A club statement read: "Manchester City FC can confirm that Saturday's Barclays FA Women's Super League fixture against West Ham United has been postponed.
"The Football Association have decided to postpone the match following four positive COVID-19 cases and a number of other mitigating factors affecting the City squad. A new date for the game will be confirmed in due course."
A West Ham statement added: "The health, safety and wellbeing of the players and staff at both clubs is the overriding priority for West Ham United, Manchester City and the FA.
"West Ham United will now work closely with Manchester City and the FA to arrange a new date for the fixture, which will be confirmed in due course."