The games between Hull FC and Leigh Centurions and Hull KR's home clash with Warrington Wolves were both postponed this morning (Saturday).
Castleford Tigers' visit of Salford Red Devils and Huddersfield Giants' trip to Wigan Warriors will both go ahead.
A statement from the RFL and Super League confirmed: "Hull FC have postponed their match against Leigh Centurions after a third member of their senior squad tested positive, with a fourth symptomatic player awaiting the result of a PCR test.
"Four more members of their top-25 paid players are also required to isolate as close contacts, taking them to the threshold of seven senior players unavailable as a result of Covid-19 which permits a postponement."
It added: "Warrington Wolves have postponed their match at Hull KR with four players in their senior squad now either confirmed positives or symptomatic, in addition to three more required to isolate as close contacts – again taking them to the threshold of seven.
"Two non-playing staff members have also tested positive."
The statement insisted the clubs affected had tried to get the games on.
"Both Hull FC and Warrington have additional players from outside their top-25 ruled out through either positive tests or as close contacts," it said.
"[That] in addition to a number of other selection issues has frustrated their attempts to do everything possible to fulfil the fixtures, notwithstanding the Covid Fixture Protocols.
"The clubs will now liaise with the RFL about a possible rearrangement of the fixtures - although the Betfred Super League table will again be determined by win points percentage to allow for the possibility of not all fixtures being fulfilled."
Coronavirus outbreaks at a number of Super League clubs have wreaked havoc with the fixture list in recent weeks, with Huddersfield, Leeds Rhinos and Salford Red Devils among those having games postponed.
In addition, both Castleford and Giants have had to forfeit matches because of injury problems, with their opponents being awarded a 24-0 win.
The latest postponements mean every club in the competition has now had at least one game delayed or cancelled.