Premier League clubs must have at least four Covid-19 cases within their squad to apply for a postponement under new criteria.
The league confirmed the change to the rules, which have been criticised in recent weeks, after a meeting of clubs on Wednesday.
The league said the rules would take effect before the next Premier League fixture, the rearranged match between Burnley and Watford on 5 February.
Under the previous rules, if a club could not field 13 outfield players and a goalkeeper from their squad list or appropriately experienced under-21 players, the match would be postponed. However, this could include absences unrelated to Covid-19, such as injury or international duty.
There have been 22 postponements in the Premier League under the coronavirus criteria since the Omicron variant led to an increase in cases among players and staff.
The league also said its Covid-19 emergency measures – which cover testing, treatment time, the wearing of face coverings and the observance of social distancing – would be reviewed weekly with a view to their expiring no later than 28 February.