Drivers in London will be required to submit a photograph of themselves to verify they are following the new rule before they can begin working.
Passengers and drivers will be allowed to cancel a trip without financial penalty if the other party is not wearing a face covering.
Uber’s policy is in line with the Government’s decision to make face coverings mandatory for public transport users in England from Monday.
Drivers will also be asked to confirm they have taken additional safety measures such as regularly sanitising their car and washing their hands.
Jamie Heywood, Uber’s regional general manager for northern and eastern Europe, said: “For months we’ve been urging people to stay home, for their safety and the safety of drivers who make essential trips.
“Now, as cities begin to reopen and people start moving again, we’re taking measures to help everyone stay safe and healthy every time they use Uber.
“We’ve introduced measures to ensure that every driver can access the PPE (personal protective equipment) they need for free to help keep them safe when driving with Uber, and from Monday, we will require anyone using the Uber app in the UK to wear a face covering.”
The requirement for drivers to provide proof they are wearing a face covering could be extended from London to include the whole of the UK, Uber said.
Other safety and hygiene measures introduced by the firm include trialling in-car partition screens in Newcastle, distributing more than two million masks to drivers and couriers, and sending 54,000 units of cleaning spray and hand sanitiser to drivers.