Two of Friday's Super League three scheduled games, Huddersfield against Castleford and Warrington versus Salford, have been cancelled.
The Giants game was axed after the Tigers revealed 12 positive Covid-19 tests within the club.
Salford have also forfeited their game, with a 24-0 win applied to their opponents, after reporting just 13 players were fit for selection.
Warrington and Huddersfield will play their round 21 game on Friday instead.
The Salford case will be referred to the Rugby Football League compliance team.
In the case of Castleford, the RFL and Super League will liaise with Public Health England, the Tigers and their last opponents Leeds, before the Multiple Case Group discusses the next steps.
Leeds have confirmed their game with Wakefield will go ahead on Thursday, despite four track and trace flags, which rules out those players for four games.
Castleford's tests took place on Tuesday.
Super League and RFL will make another announcement "as soon as practicable".
Further results of this week's testing programme at all clubs will be provided as soon as complete information is available.
Friday's postponements follow the cancellation of Monday's match between Catalans and Warrington, which was called off because of a spike in Covid-19 cases at the French club.
Warrington have not played since 13 October, as they have had a bye-week when scheduled to play withdrawn club Toronto and then had their trip to Perpignan postponed.
The Super League table was adjusted following the resumption of play to allow for the prospect of games being cancelled because of issues related to the fixture schedule and Covid-19.
Clubs must play a minimum of 15 of a possible 20 games to qualify for the play-offs, with four places available based on win percentage - a figure acquired by taking the number of wins, divided by the games played and multiplied by 100.
Neither Huddersfield or Castleford are likely to acquire a high enough win percentage to make the top four, with 43.75% and 37.5% figure.
Leeds are one of the hopefuls, with 60% opposed to Catalans who have played only 12 games and have 66.67% figure in fourth.