In addition to the lawsuit, which was filed in Franklin County Municipal Court today, the city attorney's office is asking for a temporary restraining order that would prevent UberX from operating until a judge can decide whether to grant a permanent order.
In February, UberX and a similar company, Lyft, launched in Columbus with promotions to provide free rides.
Both companies use smartphone apps that help users find a ride in a driver's personal car and to pay for the ride using a credit card. The app calculates the fare, and the companies keep a portion of the payment.
But city officials have said charging for the rides is illegal because drivers are acting as unlicensed vehicles for hire, a minor misdemeanor.
The lawsuit also argues that public safety is at risk because the city cannot verify drivers' backgrounds or conduct vehicle inspections.
UberX representatives could not be reached for comment.
"Basically, we have confirmation UberX is charging, which puts them in direct violation of the city code," said Amanda Ford, spokeswoman for the city Department of Public Safety.
The UberX app debited payments from a checking account used in a city investigation at least six times, according to the lawsuit.
The city also is investigating Lyft, Ford said. "Once we have what we need on the Lyft side, we'll move forward with them as well."
Both apps started operating this year before the city could finish regulations that would require the companies and their drivers to obtain city licenses. City officials have been tweaking the proposed rules, which must be approved by Columbus City Council.
The court filing does not affect UberX's other service, Uber Black, which uses local licensed livery drivers who provide trips in luxury vehicles. The city changed its code to allow that service to operate.
The local taxi and livery industry has argued that the companies do not have adequate insurance and should have to follow the same rules as other for-hire vehicles.
Uber and Lyft have faced similar opposition in other states as well.
"Would you get on an airplane that wasn't properly inspected?" said Morgan Kauffman, who owns Yellow Cab of Columbus. "There's no chance in the world, and there's far more car accidents than plane accidents."