The driver, who asked not to be identified, said she had originally agreed to pick up a woman at Westheimer and Montrose Saturday evening, so she was surprised when two men got in.
"I said, 'Are you Christine?' and they said, 'a lady ordered the ride for us,'" she said.
The victim said she drove the men to a church less than a mile away.
"When we got to the drop-off point, they asked me to drop them off on the side of the church," she said.
She ended up pulling over at the corner of Hyde Park and Van Buren, where she said the men began attacking her from the backseat with a rock.
"They just hit me and grabbed me and just hit me again, and it just - it was very fast," she said.
In a bid to escape, she said she flung open her car door and rolled out onto the street.
One of the men got in the driver's seat, and both suspects drove away.
Police said they spotted the vehicle six miles away in the 1400 block of Lockwood later that same night.
They said the suspects crashed into a tree while fleeing from officers.
Isaac Johnson and Christopher Carrington were both charged with aggravated robbery with a deadly weapon. Carrington also faces an additional charge of evading arrest with a vehicle.
The victim said she had only begun driving for Uber three months ago to support her children amid a divorce, but is now rethinking that decision.
"We can't discriminate because it counts against us and, you know, if I'm traumatized by people with face tattoos, I should be able to say no to people with face tattoos," she said.
On Monday, Uber sent the following statement regarding the incident:
"What this driver experienced is terrifying. We've been in contact with the driver to check on their wellbeing, and are standing by to assist law enforcement however we can in their investigation."