The incident follows a backlash against app based cab services after a woman was allegedly raped by an Uber driver.
Ola said the driver was dispatched by its partner company TaxiForSure, which it acquired for $200m (£130m) in March.
"I was about to make a call when I noticed that he was masturbating while driving. He had little control over the wheel as well as his perverseness.
He had a smile on his face that will haunt me for nights to come. A #PSYCHOTIC man with a severe chemical imbalance for a driver is nothing but serious," the woman wrote in a Facebook post.
The Hindustan Times newspaper quoted the CEO of TaxiForSure as saying that the driver had been blacklisted and his services terminated based on the complaint. He added that the driver had a clean record so far.
App based aggregator services have been criticised in India for not doing proper background checks on drivers they recruit.
In December, a woman in Delhi alleged that the driver of her Uber cab had raped her after she fell asleep in the backseat of the car.
The Delhi government immediately banned app based services, with several other states following suit. The Uber cab driver is currently facing trial and has denied all the charges against him.
However, they recently came back on the roads after Ola managed to successfully convince the Delhi high court to overturn the ban.
Ola was valued at $2.5bn (£1.6bn) in April, following a fresh round of funding.