The number of positive cases has left the club unable to field a side for today's match.
A club spokesperson said: “The club can confirm that our cinch League one fixture against Alloa Athletic, scheduled to kick-off at 3pm Sunday 2nd January, has been postponed.
Due to a number of COVID cases we do not have sufficient players available to fulfil the fixture.
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A new date for the match is still to be confirmed but we will provide an update for supporters when we are able to.”
An SPFL spokesperson said: “The SPFL can confirm that following requests from Falkirk and Cowdenbeath, their games this afternoon have been postponed.
The clubs do not have sufficient players available to fulfil the fixtures because of Covid cases. New dates for the matches will be confirmed in due course.”