The woman, identified only as Jane Doe in the lawsuit filed in federal court in California, said in the complaint that she was "violated physically" when she was brutally raped in Delhi by her Uber driver in December 2014.
"Sadly, in the United States, Uber executives violated her a second time by unlawfully obtaining and sharing her medical records from that vicious sexual assault and have failed, as of the date of this filing, to apologise to her for this outrageous conduct," the lawsuit said.
The lawsuit has been filed against Uber, Kalanick, Uber's former Vice President for Business in Asia Eric Alexander and the company's then-Senior Vice President for Business Emil Michael.
The lawsuit has been filed days after it emerged that Alexander had obtained medical records of the 26-year-old woman and had shown them to Kalanick and Michael. It is also alleged that numerous executives at the car-hailing company were either told about the records or shown them by this group and Alexander had carried around the document for "about a year" before other executives, "presumably the legal department, obtained the report and destroyed his copy."
It is also alleged that Alexander, Kalanick and Michael had considered the prospect that Uber's main rival in India, Ola, could have been behind the sexual assault incident to sabotage the company.
The lawsuit added that Uber executives "duplicitously and publicly decried the rape, expressing sympathy for plaintiff, and shock and regret at the violent attack, while privately speculating, as outlandish as it is, that she had colluded with a rival company to harm Uber's business."
The woman currently lives in Texas and had previously sued Uber in 2015 for its lack of sufficient safety standards.
The case was settled a few months later.