The meeting will be rescheduled for next Monday at a larger venue, the city's recreation center.
Wolfe faces a felony charge for abusing his power.
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According to court documents, Wolfe allegedly owed more than $10,000 in delinquent utility bills. His daughter owes more than $9,000.
After an independent audit of the city found financial inconsistencies, the Texas Rangers say they uncovered proof Wolfe routinely intervened to prevent utility cut-offs despite delinquent bills.
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The city runs the local utility. Court documents say Wolfe admitted to providing extensions to some residents, including his daughter and himself.
Wolfe was released on a $5,000 bond after his arrest Thursday.
Many residents went to the city council meeting to vent their frustrations.
"Our mayor stole from us. Pure and simple," said Mary Ann Drawl. "He admitted it. So he needs to step down."
Wolfe says he's not resigning.
"I respect the opinions of the people. I've always respected that," Wolfe said.