Five members of Eagles’ playing staff have also been identified as close contacts of the players who tested positive and are now isolating.
Seven players being ruled out for Covid-related reasons is the minimum which permits the postponement of a fixture under the RFL’s protocols.
Eagles, who lost to Batley Bulldogs last Friday, have also called off their scheduled training sessions for the rest of this week.
It is the first time a Championship fixture has been postponed because of positive Covid tests and the first rugby league match at any level called off this year for that reason, though travel restrictions prevented Featherstone Rovers making the trip to Toulouse Olympique two weeks ago.
The game at the Shay will now go ahead on the weekend of June 5-6, which is one of two available match slots for rearrangements during the Championship season.
This year’s Championship table will be decided on win percentage because of the pandemic.