The child of one of the Bulldogs players attends a school in the Sutherland Shire where a staff member has tested positive for Covid-19.
The primary school has closed until 25 June and students have been told to self-isolate.
The Bulldogs and Roosters game will now be played on Monday night at Bankwest Stadium due to the potential biosecurity problem.
Sunday's later game between St George Illawarra and Cronulla at Campbelltown Stadium has been brought forward to the earlier timeslot.
The Australian Rugby League Commission approved changes to the Round 5 schedule to ensure the health and safety of the playing group and community after a remote risk to the Bulldogs squad emerged.
ARL chairman Peter V'landys said while the risk the virus had spread to the Bulldogs playing group was remote the Commission wanted absolute certainty before allowing the team to play.
"There's a very remote risk of infection within the Bulldogs squad. To ensure there is no risk at all, the player will be tested today and the game delayed until tomorrow to ensure the test results have returned. I want to congratulate the Bulldogs for swiftly informing the NRL,'' he said.