Pennsylvania state authorities have arrested and charged a Harrisburg man they said set fire to the governor’s mansion while Gov. Josh Shapiro and his family slept, forcing them to evacuate early Sunday before the blaze severely damaged part of the building.

The man, identified as Cody Balmer, 38, jumped a fence and managed to evade state troopers after he broke into the building, the authorities said. He fled the scene and was arrested after turning himself into police on Sunday afternoon, officials said at a news conference.

Mr. Balmer was charged with attempted murder, arson and terrorism, the Dauphin County District Attorney’s Office said early Monday.

During a news briefing on Sunday outside the fire-scarred mansion, Governor Shapiro, a Democrat who gained national prominence last year when he was on the short list of possible running mates for Kamala Harris, said that the F.B.I. was assisting in the investigation. The smell of smoke lingered in the air as he spoke, with the blackened, broken windows where the arsonist had struck visible behind him.

Mr. Shapiro became emotional as he described his family’s ordeal, recalling the moment a state trooper had banged on his door shortly after 2 a.m., waking him, his wife and his children, and rushing them to safety. The attack, he said, had been “targeted.”

“Last night, we experienced an attack, not just on our family, but on the entire Commonwealth of Pennsylvania,” Mr. Shapiro said. “I want you all to know that your prayers lift us up, and in this moment of darkness, we are choosing to see light.”