The move follows recommendations made after a review of management and practices at the firm.
The report was sparked by a former employee's claims the company ignored her complaints about sexual harassment and gender discrimination.
Uber's board voted unanimously in favour of the recommendations on Sunday.
Some of Mr Kalanick's responsibilities could be shifted to other executives.
In the email to staff, Mr Kalanick said his decision to take leave, which also comes after the sudden death of his mother in a boating accident, is part of an effort to create "Uber 2.0".
"For Uber 2.0 to succeed there is nothing more important than dedicating my time to building out the leadership team," Mr Kalanick wrote. "But if we are going to work on Uber 2.0, I also need to work on Travis 2.0 to become the leader that this company needs and that you deserve."
Mr Kalanick's email did not say how long he would be away from the firm.
Uber has been rocked by a series of controversies in recent months, including an investigation of its business practices and a lawsuit from Google's parent company, Alphabet, over alleged theft of trade secrets related to driverless cars.
Criticism of its aggressive corporate culture has also circulated, inflamed earlier this year when Mr Kalanick was caught on video berating an Uber driver.
He said in response to the video: "I must fundamentally change as a leader and grow up."
Uber: Travis Kalanick's rollercoaster reign
His leave follows the departure of other high-ranked executives.
Uber last week also said it had fired more than 20 staff and taken actions against others following a separate review of more than 200 human resources complaints that included harassment and bullying.
"Implementing these recommendations will improve our culture, promote fairness and accountability, and establish processes and systems to ensure the mistakes of the past will not be repeated," said Liane Hornsey, the firm's chief human resources officer.
"While change does not happen overnight, we're committed to rebuilding trust with our employees, riders and drivers," she added.
Mitch Kapor and Freada Kapor Klein, investors in the company who had pushed for change earlier this year, called the recommendations "thoughtful and extensive" and suggested the company was taking the issues seriously.
"Our stated hope all along was that Uber could leapfrog other companies to be a real leader in diversity and inclusion," they said.
"At this point we believe that the company deserves some room to put the plan into effect and show us what can be done."