Mr. Bush was in his limousine Saturday ready to leave the building when the incident happened, a senior administration official said. He left the arena less than five minutes later from an exit about 40 yards from the car.
Authorities swarmed the car with weapons drawn and took away the driver and her children. Secret Service and local law enforcement investigators concluded after interviewing her that she had no intention of harming the president, said Ann Roman, a Secret Service spokeswoman.
"Essentially, she was trying to locate her mother-in-law, who was attending the president's speech," said William Jenkins, the FBI's acting special agent in charge in Jackson.
The woman, who was not carrying any weapon, was arrested for trespassing, Roman said in Washington, D.C.
A law enforcement official, speaking on condition of anonymity, identified the driver as Betina Mixon, 29, of Horn Lake.
Mixon, a nurse's aide and the mother of three sons, had been under stress recently because of marital problems and a hysterectomy, said her friend Amy Graves, of Walls.
"She just snapped," Graves told the DeSoto Times for its online edition Saturday.
Another friend, Lisa Jones, told the paper the incident was "absolutely not" politically motivated. "She is not that type of person," Jones said.
Witnesses said a gray Toyota Camry drove through a parking lot on the same side of the DeSoto Civic Center as the president's exit. The car jumped the curb, drove through a gate where press buses had just left and rammed the building near a loading dock.
"We heard sirens and looked and the car was flying around the corner," said Michael Smith, 17, who was on the loading dock with about a dozen workers taking a break from their food service jobs at the center.
"As soon as the car hit the wall, there were probably 20 cops on her," Smith said.
Damage to the front of the car indicated it hit the building at 5 to 10 mph (8 to 16 kph). No ambulances were called to the scene.
Police rushed the car, dragged out the woman, handcuffed her and whisked her away.
No shots were fired from or at the car, White House spokesman Trent Duffy said. "There was a vehicle that did crash into the side of the building," Duffy said, although it was "not close" to the president's car.
"The president was never in any danger and is keeping with his schedule," Duffy later told reporters aboard Air Force One as Mr. Bush flew to Paducah, Kentucky.
He would not say whether Mr. Bush saw what happened or say what the president's reaction was.
DeSoto County sheriff's Capt. Bill Rasco said the woman was taken to the DeSoto County jail, where she was being questioned by the Secret Service.
Mr. Bush had spoken at a rally for Republican gubernatorial candidate Haley Barbour, the first of four campaign speeches Mr. Bush had scheduled for Saturday.