At the end of the 30-kilometre trip, he pulled the driver from behind the wheel.
On his Twitter account, the bemused customer shared footage and images of the driver asleep in the passenger seat.
The tech giant told Indian site The News Minute that the driver had been removed from the platform.
"This is a regrettable and concerning incident," an Uber spokesman said.
"While we take all possible measures to ensure that drivers behind the wheel match the person shown on the app, in rare instances, when this doesn't happen, we encourage riders to cancel their rides immediately and report the issue on the app.
"Upon learning about this incident, the driver profile was removed from the app and we are looking into the matter."