Springsteen had already exceeded the 10:30 p.m. curfew by half an hour Saturday night when he welcomed McCartney on stage and the pair sang a pair of Beatles hits.
But the microphones were turned off before they could thank the crowd, forcing them to leave the stage in silence.
A statement from concert organizer Live Nation said it was unfortunate that Springsteen's three-hour-plus performance was stopped "right at the very end," but it said that the curfew had been laid down by the authorities "in the interest of the public's health and safety."
Huge concerts in Hyde Park, a 350-acre (140-hectare) expanse of landscaped garden and parkland that abuts some of London's wealthiest neighborhoods, have increasingly caused friction between fans and the area's well-heeled residents, many of whom gripe about the late-night noise and nuisance.
"English cops may be the only individuals left on earth that wouldn't want to hear one more from Bruce Springsteen and Paul McCartney!" he wrote on Twitter. "On a Saturday night! Who were we disturbing?" Finally he added: "There's no grudges to be held. Just feel bad for our great fans. ... It's some City Council stupid rule."
London mayor Boris Johnson, said Sunday that the singers should have been allowed to keep going, telling London radio, "You won't get that during the Olympics.