Up to the end of November, 296 complaints were made relating to hackney carriage and private hire vehicles in the city - 155 of which related to the ride-sharing firm.
However, just four related to drivers for the firm that had been licensed by York council - leading to fears that Uber vehicles are coming into the city from other areas.
Councillors also cited a data breach which affected millions of users of the app worldwide. Uber will be able to appeal against the decision at Magistrates' Court.
Hackers were able to obtain the names, email addresses and mobile phone numbers of passengers and drivers, the taxi-hailing firm said.
But the cyber attack, which affected 57 million customers and drivers worldwide, was not initially reported by the company after it hushed up the scandal.
According to the Yorkshire Post, licensing committee member Councillor Dave Taylor said during the meeting: "This city needs to have control of its taxi services and it needs to have a level playing field and I don't know if that means then national legislation aught to be tidied up.
"But I don't think that we can license a company which directs drivers to go around the houses, pumping up fair for customers, that tries to claim it has no liability for any claims, demands or losses, which claims to have a local office but never seems to staff it and the number of complaints against them is so high.
"I think those are the grounds on which we can refuse this licence."
A spokesman said: "The application by Uber Britannia Ltd to renew its private hire operator's licence in York has been considered by City of York Council's Gambling, Licensing and Regulatory Committee tonight.
"Applying the legislation, the committee has decided to refuse the application having concerns about a data breach currently under investigation and the number of complaints received."
Uber has pledged to clean up its act and make changes as it battles to regain its licence in London.
The company's concessions are likely to involve passenger safety and benefits for its drivers, possible limits on working hours to improve road safety and holiday pay.
The move came as more than 650,000 people signed a petition urging Transport for London to reverse its decision to remove the firm's licence in the capital.
A spokesman for Uber said around 20,000 of the firm's drivers had emailed Mr Khan directly to object to the decision.
TfL sensationally stripped the global taxi app of its licence to operate in London on Friday, claiming it was not "fit and proper".
Tom Elvidge, Uber's general manager in London, said at the time of that decision: "We'd like to know what we can do...to sit down and work together to get this right."
TfL took the decision not to renew Uber's licence following concerns about the tech giant's failure to report serious crimes by drivers and the firm's vetting process.
Labour leader Jeremy Corbyn backed the action, saying the body had looked at the firm and "expressed very serious concerns".
But some MPs accused London Mayor Sadiq Khan of relenting to union pressure.
He had been given £30,000 for his mayoral campaign by the union that represents black cab drivers.
GMB, which has almost 640,000 members and campaigned for years against Uber's presence in London, has called the ban an "historic victory".
However, Khan – who as mayor is chairman of the Transport for London board but did not take part in the licensing decision – said Uber had brought the ban on itself.
