The ride hailing app made the announcement to customers on Friday and said a new feature in the app will require drivers to upload a selfie of themselves wearing a mask before they can start work.
The company said any passenger who arrives without a mask can be refused entry to the vehicle, and that passengers can cancel a ride if a driver arrives without wearing one.
The new rules come as Transport for London, which licenses cabs and private hire cars in the UK capital, urged taxi companies to require drivers and passengers to wear face masks.
It said the rules would apply to all taxi companies -- including London's famous black cabs -- and masks would be mandatory for all passengers, except children and those with breathing difficulties, in line with national guidance around their use.
Uber told passengers in an email on Friday: "We're introducing mandatory face coverings as of Monday, June 15th to help protect the health and safety of you and your driver. As of Monday, if you aren't wearing a face covering, your driver has the right to cancel your ride, and anyone who is repeatedly flagged for not wearing a face covering will risk losing access to the app."
Uber already requires drivers and passengers to wear masks in several other countries, including the US.
Addison Lee, a major London taxi company with a fleet of 4,000 vehicles, also said it would adopt the rules from Monday, alongside clear shatterproof "safety screens" for added protection.
From Monday, as part of measures unveiled June 4 by Transport Minister Grant Shapps, passengers across England will be required to wear masks on public transport including trains and buses, where it is often not possible to stick to the two-meter social distancing guidelines.
However, those rules did not include taxis, making London the first region of the country to extend them to apply to private transport hire vehicles.