It comes after a review of management and practices at the firm, which is facing a number of scandals including complaints of sexual harassment.
Uber's board on Sunday voted in favour of the recommendations from the review.
But two days later, board member David Bonderman made a sexist remark at a meeting about the recommendations and has now stepped down.
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."