The Premiership, which has been suspended since March, will resume this week but games will be played without fans as part of measures to curb the spread of the novel coronavirus.
The Chiefs, one of the few clubs to have consistently posted profits in the last few years, were losing more than £1m each month, Rowe said.
"I don't think the rugby fraternity realise how much clubs are losing," he said. "We still have to maintain all the infrastructure, as well as the playing side, so it's been incredibly difficult.
"Most of the clubs will have worked out how long they can survive but, if we can't get some decent revenue coming in by the new year, we've got serious problems.
"At Exeter ... we're fortunate we've been able to lean back on some of our assets to help raise the funds we need to keep going, but I do fear for some of the other clubs."
Rowe said clubs had been hit particularly hard by the loss of matchday revenue.
"Central funding is made up of TV, league sponsors and RFU money. However, the bigger money comes from bums on seats and if we can't get spectators into the stadium, we're all going to be in trouble," he added.
The Chiefs, who are top of the Premiership, will resume their season against Leicester Tigers on Saturday 15 August.
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