The blaze in the rear of the two-story white frame house in Hope was reported by a passing motorist at 3:17 a.m. Friday, according to J.R. Wilson, police chief of the southwestern Arkansas city.
The fire appeared to originate at the base of an exterior wall and rose about 8 feet midway up the house, Wilson said.
A National Historic Site, the house belonged to Clinton's grandparents and he lived there for four years after his birth in 1946, according to Arkansas' state website.
"The building is in good shape, (and) the fire department extinguished the fire very quickly," Wilson said.
Smell at the scene indicated an accelerant may have been used, Wilson said.
Tarona Armstrong, the home's superintendent, said in a statement that the fire was confined to one portion of the house.
"At this time the extent of damages and the cause are unknown until the ongoing investigation is completed," the statement said. "The house will be closed until further notice."
Graffiti on walkway, door
In addition to damage from any flames, the home's walkway and a door were vandalized with spray-painted graffiti.
The number "55," left in black paint on a walkway, could refer to a common text messaging abbreviation for "haha," Wilson said.
On the door, "XX" was spray painted "and just right below ... a big frown and a big, long protruding tongue sticking out of the frown," Wilson said.
Investigators were collecting video from surveillance cameras in the area, Wilson said.
The National Park Service is investigating the cause, and the FBI has offered assistance, Wilson said.
And a spokesperson for the Bureau of Alcohol, Tobacco, Firearms and Explosives said that a fire investigator from that federal agency's New Orleans office should arrive on scene Saturday to assist local authorities.
Mayor: Home should be seen as history
Dennis Ramsey, the mayor of Hope for 22 years, said the house represents "a legacy in small town America."
"The prospects of a president coming from a small town in southwest Arkansas -- What were the chances of that? -- but it's something of which we are very proud," he said.
Ramsey called it "very fortunate that someone was up at that time and happened to see it before it caused significant damage."
While he has been out of office since January 2001, Clinton remains in the spotlight as his wife -- Democratic frontrunner Hillary Clinton -- runs to become president herself.
The 2016 election has stirred strong feelings in Arkansas and elsewhere, just like Bill Clinton himself. But Hope's mayor said that politics should be secondary when it comes to Clinton's old house, which he described as "something to be proud of and to build a legacy upon."
"To see it demeaned in this way," Ramsey added, "is an affront to all of the country and especially all of us in southwest Arkansas who are very proud to be from a place called Hope."
Friend: 'Clinton birthplace is the comeback house'
The house is furnished with items dating to the time when Clinton lived there, according to the state website.
Clinton moved to Hot Springs when he was 7, the website said. But the Hope home was the center of his family life -- he spent summers and weekends there -- until his grandfather, Eldridge Cassidy, died in 1956 and the house was sold.
The would-be Arkansas governor and president remembered "playing in the yard with friends and learning from his adored grandfather about social justice and the equality of all people," according to the National Park Service.
In 2011, the home was officially designated as a National Historic Site within the national park system.
Skip Rutherford, dean of the University of Arkansas Clinton School of Public Service, called the building "a premier educational, historical and tourism anchor for Hope and like all presidential birthplaces it also is important nationally.
"It has been restored before, and it will be restored again," Rutherford, who has been friends with Bill Clinton since 1974, said of the home.
"If Bill Clinton was the comeback kid, then the Clinton birthplace is the comeback house."