The crane operator was taken to a hospital with injuries but no one else was hurt.
The collapse came four days before President Barack Obama's scheduled speech inside the cathedral to observe the 10th anniversary of the Sept. 11 terrorist attacks. The speech is the highlight of three days of events set to start Friday at the cathedral.
No immediate decision was made about whether the commemoration, which also includes a concert and vigil, would go on as planned, said Richard Weinberg, a spokesman for the cathedral.
The crane was being used to repair the dings caused by the East Coast earthquake Aug. 23. The cathedral's limestone exterior towers and some interior areas were damaged. It has been closed to visitors during repairs.
The crane, based on the bed of a tractor-trailer, toppled around 11 a.m. and slammed into the parking lot, damaging at least three cars. Images showed the crane lying on the parking lot, the tractor-trailer's wheels pointing to the sky.
Weinberg said the crane damaged Herb Cottage, which houses the cathedral's gift shop. The crane also fell near the Church House, which is used by members of the diocese. The 20 people inside the buildings were not hurt, Weinberg said.
"If it had gone any other direction it would have hit another building, which would have been bad," fire Battalion Chief John Donnelly said.
Engineers were investigating what caused the crane to tip over, and representatives from the Occupational Safety and Health Administration were on the scene. Fire officials cautioned that removing the crane from the cathedral grounds would be cumbersome.
The cathedral is one of the nation's most recognizable places of worship, holding funerals for several U.S. presidents and a memorial service for victims of the Sept. 11 terrorist attacks.
Sheryl Wilcox, an event manager for the Episcopal Diocese of Washington, said she was in Church House when she was startled by a noise.
"I heard what it sounds like now -- thunder -- or I thought something had fallen out of the construction truck," Wilcox said.