Face masks have been required in taxis and on public transport for the past year to reduce the spread of the virus.
But Uber has said it will keep its "no mask, no ride" policy in place.
That's despite rules in England being replaced with guidance advising people to wear masks in enclosed spaces.
Uber said the policy was for the safety of both its passengers and drivers, although it will not apply if people are exempt.
"As cities continue to open up, we will ensure that face coverings or masks continue to be a mandatory requirement, unless exempt, when travelling with Uber across the UK," the ride-hailing firm's UK general manager Ash Kebriti said.
Uber is the latest transport operator to announce that masks will continue to be mandatory on its services after Monday.
London Mayor Sadiq Khan has declared masks mandatory on public transport in the capital and Greater Anglia has said masks will remain compulsory on its services.
Mayors including Greater Manchester's Andy Burnham and West Midlands' Andy Street have urged passengers to continue wearing face coverings but do not have the power to make it mandatory.
The government has previously said masks were still "expected and recommended" in crowded indoor areas, but people in England will not be required by law to wear them from Monday.
Some airlines have confirmed that masks will still be compulsory after 19 July, while other businesses such as shops, restaurants and pubs are still setting out their plans.
On Friday, pub chain Wetherspoons said it planned to retain floor screens between tables, one-way systems and limits on the number of people in its pubs. But it said that customers and employees would be able to choose whether they wear a mask.
Meanwhile, the Co-op has said face coverings will only be "strongly encouraged" in its supermarkets, rather than mandatory.
In Scotland, the mandatory use of face coverings will remain in place for "some time", First Minister Nicola Sturgeon has said, even after the country eases most of its other restrictions on 19 July.
In Wales, masks will continue to be required by law in some settings, including public transport.