"We have forfeited racing today due to damage to our wing, we will be back tomorrow (Tuesday) to fight another day," the British team said on Twitter. The team has a spare wing which it is allowed to use under the America's Cup rules.
Ainslie's America's Cup challenger crew, who are seeking to bring the trophy "home" to Britain, was forced to quit after hearing a "bang" during what was set up to be a tight race against New Zealand.
The British skipper abruptly halted his 50-foot foiling catamaran to prevent further damage after completing only the second of seven legs in the widely-anticipated first race.
New Zealand helmsman Peter Burling had got the better of Ainslie at the start and led to the second mark of the course, but the British boat appeared to be catching them.
Conditions were perfect for the high-octane sailing boats following disappointment on Sunday when racing was postponed because of a lack of wind.
"A bit of a shame for those guys ... it was shaping up to be a good race," New Zealand helmsman Peter Burling said in televised comments after the British crew retired.
In the other semi-final, Artemis Racing and SoftBank Team Japan finished the day level after some thrilling racing.
The Japanese crew skippered by Dean Barker recovered from a shaky start in the first race to beat the Swedish team, but after nailing the start of the second, Barker's crew made a series of small mistakes and threw away a substantial lead.
The Japanese crew were also overhauled several times during the Louis Vuitton America's Cup qualifying event, which ended on Saturday, raising questions about their consistency.
The first team to win five races in each semi-final will go through to the challenger final at the weekend.
This will decide who gets to take on defender Oracle Team USA for the "Auld Mug", the nickname for the trophy first won by the schooner "America" off the south coast of England in 1851.
(Reporting by Alexander Smith in London; Editing by Ken Ferris, Larry King)
