The blaze in the city of Hope slightly damaged one interior room before it was extinguished, police say.
Arson is suspected because accelerant was detected at the scene. Graffiti is also being examined.
The former president spent his first years in the house, which was designated a National Historic Site in 2011.
Hope Police Department chief JR Wilson said a motorist spotted flames on the Christmas Day, according to the Associated Press news agency.
JR Wilson said firefighters saw flames 8ft high on one side of the property when they arrived.
Bill Clinton was America’s 42nd president, serving from 1993 to 2001.
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