Cameron Smith has called for the NRL to be suspended for a few weeks, claiming he and his Melbourne teammates are concerned for their families' health.
The NRL is planning to continue on into round two next weekend in front of empty stadiums, as it battles with how to deal with the coronavirus pandemic.
Melbourne is due to host Cronulla on Saturday night at AAMI Park, after sweeping aside Manly 18-4 on Sunday at Brookvale Oval.
But the game's biggest name does not believe the show should go on, claiming he is speaking on behalf of his Storm teammates when calling for the competition to be stopped.
"This thing is bigger than rugby league," Smith said.
"This affects more than just rugby league and rugby league players ... after finishing these matches on weekends, we go back to our families.
"There are several players in our squad who are going back to their families who have newborn babies.
Melbourne Storm coach Craig Bellamy speaks with Cameron Smith. Source: AAP
"Craig (Bellamy) has an elderly mother. My parents are in their 60s. Craig is in his sixties. But listening to medical advice, he is in the risk bracket.
"If we make a decision to suspend the competition for a couple of weeks, it gives everyone an opportunity to sum up the situation a lot better rather than being reactive daily or hourly."
The NRL is desperate to keep games on the field to assist with the financial side of the game, warning of a doomsday scenario if it doesn't.
The league, however, did concede on Sunday if players wanted to self-isolate, they could, although Smith said he was not at the point of sitting himself out.
But the game's most-capped player highlighted his concerns around air travel and, most notably, the amount of people at airports.
Melbourne flew home on Sunday night via a commercial airline, however the NRL is speaking with a biosecurity expert to consider whether chartered flights or buses would be safer from next weekend.
"There is something in place tomorrow to avoid being around groups larger than 500 people," Smith said.
"And there are more than 500 people at airports and we're going to be doing that every second week."
Smith also questioned how the NRL could play on if the Warriors opted to fly home to New Zealand after next week, given the 14-day isolation rules for passenger arrivals in both countries.
Manly captain Daly Cherry-Evans insisted he was happy to keep playing through the outbreak, while Melbourne coach Craig Bellamy questioned why crowds were allowed in stadiums in round one.
"If you're not going to play in front of crowds round two, you shouldn't do it round one," Bellamy said.
"I've got a mum that is 86 or 87. I've got grandkids and I want to be still hanging around them with the wife."
Crowds were already affected in the opening round.
In a sold-out stadium opening in Townsville, 22,459 fans watched Brisbane beat North Queensland, while 21,363 watched Parramatta defeat Canterbury in the season-opener.
But just 10,239 saw Newcastle go top of the table with a 20-0 win over the Warriors, while only 6325 watched South Sydney's nail-biting win over Cronulla.
Crowds of around 10,000 were also only in place for Canberra's win over Gold Coast, Penrith's shock victory over defending premiers the Sydney Roosters and St George Illawarra's loss to the Wests Tigers in Wollongong.
