A further five Sheffield players have been identified as close contacts of those infected, the club said. The match was due to be played at The Shay Stadium on Sunday.
The game was allowed to be called off because at least seven members of the Eagles squad were unavailable. This week’s training has also been cancelled.
Liam Claffey, general manager at Sheffield Eagles said he fully expects next weekend’s game against Featherstone Rovers to still go ahead, which will see the return of supporters as part of the gradual easing of lockdown restrictions.
He told The Star: “It will absolutely go ahead unless there’s an outbreak here or at Featherstone.
"We have been proactive and spoke to the Rugby Football League and we have voluntarily shut down this week just to be on the safe side.”
Claffey said he expects about 350 Eagles fans to make the journey along the M18 to watch their team in person for the first time since March 2020 on Sunday 23 May.
Doncaster RLFC are also in action at the Keepmoat earlier that day. They play West Wales Raiders, who have signed former Welsh rugby union international Gavin Henson for the 2021 season.
Sheffield Eagles remain on course for a return to the city for the 2022 season, Claffey said.
He added: “Things are on track. Everything is going well, they have done a lot of the work that probably goes unnoticed but in the next three to five weeks the steel will start going in and the foundations, and that’s when people will start seeing something happening.
"It’s coming to the stage where people will start seeing it spring up.”
The Halifax fixture will now be rearranged for the weekend of June 5-6, one of the two available match slots for rearrangements in the 2021 Betfred Championship season.
It is the first Betfred Championship match to be postponed since the competition resumed five weeks ago, and the first Rugby League fixture of any kind to be postponed as a result of positive Covid-19 tests in 2021.
Sheffield Eagles lost 18-30 to Batley Bulldogs last time out and are currently fifth in the table after five rounds of fixtures.