Exeter chairman Tony Rowe says the Premiership leaders will have major financial problems if fans cannot attend games by the end of the year.
The club were the only top-flight side to make a profit last season thanks to the conference business at Sandy Park.
But Exeter have lost £1m a month since the coronavirus pandemic forced the business to temporarily close.
"If we can't get some decent revenue coming in by the new year, we've got serious problems," Rowe said.
There have been no Premiership rugby union matches since early March after the Covid-19 lockdown and clubs voted through a reduced salary cap to lower costs, with some teams losing key stars after being unable to agree new terms.
Exeter will resume playing on Saturday when they host Leicester behind closed doors at Sandy Park as Premiership action returns.
Rowe says that while the conferencing business and central revenues from rugby - such as television rights and Rugby Football Union funding - help pay the bills, the club's biggest source of revenue is still matchday income.
"Everybody has held up Exeter as the ideal business and a profitable club because we have Sandy Park conference and banqueting that pays the day-to-day bills and then we have all these bums on seats for matchdays," added Rowe, whose leadership helped guide the club to the top flight in 2010.
"However, for the last five months that's been a millstone around our necks. At the moment we can't earn any revenue, yet our outgoings remain the same.
"What was to a degree our 'golden goose' in having Sandy Park pay the bills and the overheads, whilst the matchdays were the big earners, both of those income streams have currently gone."