Residents have complained about water quality since the city started getting its water from the Flint River about a year ago.
The council approved the motion with a seven to one vote at their Monday night meeting.
President Josh Freeman was the lone holdout.
“The resolution said ‘all things necessary,'" he said. "Well, what if one of those 'necessary things' is to raise rates 30 to 40 percent to cover that increased cost that Detroit is going to charge?”
Freeman said the council received a letter from the Detroit Department of Water and Sewerage that said Flint would be charged $850,000 per month to be on Detroit's water system.
"That's before [using] one drop of water," Freeman said.
Gerald Ambrose, Flint's emergency manager, has ultimate control when it comes to deciding whether the city will switch to a new water source.
In a press release Tuesday, Ambrose said Flint's water is as safe to drink as Detroit's.
"It is incomprehensible to me that seven members of the Flint City Council would want to send more than $12 million a year to the system serving southeast Michigan," he said.
Ambrose said that money would be better spent updating Flint's water system and reducing rates for residents.