If it decides not to appeal, the suspension will come into force.
Uber said that an “administrative error” by the council was to blame and hoped to resolve the issue soon.
Transport for London, which has criticised the firm’s record over reporting criminal offences and carrying out driver background checks, decided not to renew Uber’s London licence after it deemed the firm “unfit” to run a taxi service.
A Sheffield City spokesperson said: “Uber’s licence was suspended last Friday (29 November) after the current licence holder failed to respond to requests, made by our licensing team, about the management of Uber.
“We received a new application, for a licence to operate taxis in Sheffield, from Uber Britannia Limited, on 18 October 2017 which we are currently processing.”
The council said an operator’s licence could not be transferred and that the new application would be dealt with by the council’s licensing department.
An Uber spokesperson said: “We informed Sheffield City Council on 5 October that we would need to change the name on our licence as the named individual would soon be leaving the company.
“The council told us they couldn’t change the name on the licence, as most other councils have done, and that we would instead have to apply for a new one.”
Uber said it had submitted an application for a new licence which was still being processed.
“While we are in regular contact with the council, we did not receive the correspondence the council refers to as they sent the letters to an incorrect address,” the spokesperson said.
Uber added that if the new application could not be approved by 18 December, the firm would of course appeal against its suspension.