Leahy said the date presents a "reasonable schedule" that would give members of the committee several more weeks to prepare.
President Barack Obama has urged the Senate to vote on confirming Sotomayor to the high court before it leaves for a congressional recess in August. Republicans have pressed for more time to consider the nomination.
But Leahy, D-Vt., said there was "no reason to unduly delay consideration of this well-qualified nominee. She deserves the opportunity to go before the public and speak of her record." He said that as a judge, she will only be able to speak publicly about her record when the hearings convene.
There was no immediate response from the GOP on Leahy's announcement, which came after several days of private haggling with Sen. Jeff Sessions of Alabama, the top Judiciary Republican, on a hearing date.
Leahy said he had informed Obama by telephone about his plans and that the president "seemed pleased with the date I set."
The schedule should allow for a vote on confirming Sotomayor before the August break, Leahy said, "unless people put unnecessary delays" on the nomination.
The announcement came as Sotomayor was camped out in a Capitol office meeting with a succession of visiting senators, having scrapped plans to go see them in their offices because of a broken ankle.
Sotomayor said she felt great a day after stumbling in the airport while rushing for a flight from New York to Washington. But the judge, whose right leg is in a cast and is using crutches, opted to hold meetings in the office of the No. 2 Democrat, Sen. Dick Durbin of Illinois, rather than hobble through hallways for the eight visits on her schedule.