The council approved the pay cut for about two dozen unions working under expired contracts Thursday night by a vote of 5-2, the Detroit Free Press reported.
The cuts, which will go into effect Monday, will save the city about $470,000 a month, Mayor Dave Bing's office said.
"Historically, if you look at recent years, the unions have made sacrifices. They have come to the table. They have given up," said Councilman Ken Cockrel Jr. "The reality is, this is a step we have to take."
However, Detroit's largest union, American Federation of State, County and Municipal Employees Council 25, has filed an unfair labor practice charge to challenging the cut, meaning the council's decision will be subjected to litigation.
Meanwhile, the city of Detroit ranked first on Forbes magazine's 2013 list of "America's Most Miserable Cities."
The list, which was published Thursday, was based on statistics on a number of issues, including unemployment, violent crime, taxes and foreclosures. Detroit ranked second in 2012.
"[Detroit] is still dealing with high levels of violent crime and unemployment. Home prices, already at historic lows, plummeted a further 35 percent during the past three years to a median of $40,000 as net migration out of the city continued," Forbes said.
"The latest blow was Tuesday's announcement that the city is on the verge of being taken over by the state. Detroit is in a financial emergency and cannot pay its bills. The city has been issuing debt to fund day-to-day operations."
Bing responded to Forbes in a statement: "There is no question that Detroit has many challenges. With all due respect to the data in this report, Detroit is in the midst of a transformation. That transformation is being driven by my restructuring plan, which is focused on four key areas: public safety; public lighting; public transportation; and neighborhood blight removal."