The semifinal round will be played July 18-19, with the final being contested on Aug. 1. The games are scheduled to be held at Wembley Stadium.
Chelsea manager Frank Lampard said his young side struggled in the first half against Leicester but lauded the match would be a learning experience for them.
"We haven't played that badly since I've been back, we were fortunate at halftime that it was 0-0," he said.
While Manchester City may have lost their Premier League crown to Liverpool earlier this week, City manager Pep Guardiola said he is eager to defend the FA Cup and add more silverware. His side won the Carabao Cup earlier in March and is still alive for the Champions League.
"We are in the semifinals. It was not easy to attack against a team defending so deep but it was a good performance. I am happy to go back to London, to Wembley," Guardiola told reporters.
Manchester United needed extra time to defeat Premier League bottom-dwellers Norwich City 2-1 in a spirited match on Saturday.
"It wasn't a spectacle, we didn't threaten enough or create enough chances," said United manager Ole Gunnar Solskjaer. "But I am delighted we are into the last four and it was a good workout, we got some minutes for a lot of players. We are through and that is what counts in the Cup."