The woman appeared to be resisting arrest, according to CBS News Correspondent Mark Knoller.
The Secret Service told Knoller the president was heading to his limousine when the incident occurred, and Mr. Bush was diverted to a holding room.
The president left the arena less than five minutes later from an exit about 40 yards from the car when the situation was deemed under control, and wasn't hurt, a senior Bush administration official said.
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.
Knoller was told the car's tires were blown out when it jumped a curb.
Knoller explained that the car hit a loading dock adjacent to, but a level above where the president's motorcade was parked.
"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, Ky.
He would not say whether Mr. Bush saw what happened or what the president's reaction was.
Mike Pearson, Secret Service agent in charge of the bureau's Jackson field office, said the woman ran a police checkpoint outside the center and was in the custody of the Desoto County Sheriff's Department. The children were also taken away.
The driver was not immediately identified. A witness, Linda Neeley, 40, a teacher from Horn Lake, Miss., said the woman was white and in her 30s or 40s. She said the children appeared to be 8 to 10 years old.
Neeley and other witnesses said the woman drove a gray Toyota Camry 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.
Neeley, who was standing at the press gate taking photos, said the car "was going pretty fast," though no ambulances were called after the crash. Damage to the front of the car indicated it hit the building at 5 to 10 mph.
Police rushed the car, dragged out the woman, handcuffed her and whisked her away.
Mr. Bush was campaigning Saturday for two Republican gubernatorial candidates trying to replace Democrats in tight races in Mississippi and Kentucky, in what was seen as a test of his popularity a year before he is up for his own re-election.
The president's day planner in the South included the appearance in Desoto County and one in Gulfport, two GOP strongholds on either end of Mississippi, to lend support to former Republican National Committee Chairman Haley Barbour, who is trying to unseat Democratic Gov. Ronnie Musgrove.
Musgrove countered Mr. Bush's visit by promoting his candidacy in the Democrats' weekly radio address Saturday.
"Our leaders need to vigorously go about the business of uplifting our economy, creating jobs, improving education for our children, making prescription drugs more affordable and fighting for our troops," the Mississippi governor said.
"And they need to fight for these things as hard as they fight on the campaign trail."
In Kentucky, the president was to make two stops to lend support to Rep. Ernie Fletcher, considered the Republicans' best chance in years to capture governor's office it hasn't won since 1967.
Victory for both candidates on Tuesday would raise the number of Republican governors to 29, including California Gov.-elect Arnold Schwarzenegger, to the Democrats' 21.
RNC Chairman Ed Gillespie says the apparent strength of Barbour and Fletcher — they're ahead of their Democratic opponents in most recent polls — is a good sign for the Bush-Cheney team in 2004. He stops short of suggesting a national wave of support for Republican candidates because of Mr. Bush's standing, but he says he's confident about the GOP's chances in Kentucky and Mississippi, and a runoff election in Louisiana Nov. 15.
White House press secretary Scott McClellan twice dodged questions Friday about whether Mr. Bush is risking political capital by inserting himself into governors' races in two states he won handily in 2000 with more than 55 percent of the vote.
This is Mr. Bush's fifth trip to Kentucky and third to Mississippi.
"The president strongly supports those who share his compassionate conservative philosophy, those who are committed to improving education and strengthening our economy and committed to reaching out to faith-based groups to help people in need," McClellan said in Crawford, where Mr. Bush is staying at his ranch.
A GOP victory in Kentucky would hand Republicans the governorship for the first time in three decades. Fletcher is promoting himself as an agent of change to Democratic incumbent Gov. Paul Patton, who is barred from seeking a third term. His Democratic opponent, Attorney General Ben Chandler, is trying to convince voters that he stands apart from Patton, who admitted to an extramarital affair and is being sued by a former mistress.
"There's a little more at stake here nationally than these governors' races," said GOP pollster Neil Newhouse, who said Democrats "test-marketed their anti-Bush campaign theme" in the Kentucky race. He is working for the Republican there.
In Mississippi, the GOP has dispatched Republican leaders throughout the state to help Barbour unseat incumbent Musgrove.
Among the backers: Vice President Dick Cheney, former Senate Majority Leader Bob Dole, former New York Mayor Rudolph Giuliani, former Rep. J.C. Watts of Oklahoma, Sen. Elizabeth Dole of North Carolina, former White House press secretary Ari Fleischer and Florida Gov. Jeb Bush.