The move is in line with recommendations from a review of management and practices at the firm, which is facing a number of scandals.
The review was sparked by a former employee's claims the company ignored her complaints about sexual harassment.
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 the 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.
Analysis: Dave Lee, BBC North America Technology Reporter
When that blog post by ex-employee Susan Fowler dropped on a quiet Sunday afternoon, I doubt anybody at the company thought it would lead to this. I certainly didn't.
That moment marked the beginning of the crisis at Silicon Valley's most talked about start-up.
In the middle of it all, Travis Kalanick, a man who, rightly or wrongly, now symbolises what people feel is the very worst of tech "bro" culture. A man flush with money and an unrelenting ambition that slowed for no-one. Until now.
Uber's problems were enough, most argued, for Mr Kalanick to make this decision. But coupled with the tragic death of his mother, the 40-year-old is quite understandably not in a position to give the company the attention it so desperately needs.
Since I started reporting this story I've been told how this problem is not limited to Uber. It's across the tech industry far and wide. With that in mind, it will perhaps be encouraging to the rank-and-file at every tech firm that this fiasco began with one act: a woman brave enough to speak out.
Uber, a ride hailing company based in San Francisco, 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.
It also encountered pushback when it changed its policies around collecting user data.
Its corporate culture has been criticised for being aggressive, and this was inflamed earlier this year when Mr Kalanick was caught on video berating an Uber driver who voiced concerns about fares.
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.
The recommendations released on Tuesday stem from a broader review conducted by the law firm Covington & Burling.
The proposed changes include starting performance reviews for senior leaders, reviewing the firm's pay practices, beefing up its human resources department and installing an independent board chair.
"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.
Uber has revolutionized the taxi industry since Mr Kalanick launched the ride hailing app less than 10 years ago, clashing with authorities as he  expanded the firm to more than 600 cities and a workforce of more than 12,000.
Privately held, investors reportedly valued it last year at nearly $70bn.
But the scandals have taken a toll on the company's reputation and business, according to reports.
A Monday survey of US adults by Morning Consult Brand Intelligence found 40% of respondents had a favourable impression of the firm, down from 49% just a week earlier.
TXN Solutions, which tracks consumer spending, also says Uber has lost market share since January, when consumers began a campaign against the company for not taking stronger stance against US President Donald Trump, particularly his Muslim ban.
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."
But Susan Fowler, the former Uber engineer whose blog prompted the controversy, sounded a more sceptical note.
"Ha! Yeah, they'll never apologize. I've gotten nothing but aggressive hostility from them. It's all optics," she wrote on Twitter.
"Remember that this is not about diversity and inclusion, it's about laws being broken. Harassment, discrimination, retaliation are illegal."
Uber boss Travis Kalanick plans to take time away from the company, and could return in a diminished role.