"It's pretty logical it was purposely set," J R Wilson, the police chief in Hope, Arkansas, told AFP.
The blaze ran up an exterior back wall of the white frame house where Clinton spent the first few years of his life, but the damage was minor, Wilson said.
A motorist reported the blaze in the early hours today, which is Christmas Day, and police and fire crews arrived within minutes.
Once there, they detected a smell of an accelerant near where authorities believe the fire began.
Police are also analysing some black graffiti at the scene for possible clues.
There are currently no suspects, Wilson said.
Built in 1917, the house belonged to Clinton's grandparents and it was in its yard that the future 42nd US president played in a sandbox and on a swing set, according to the Clinton Birthplace Foundation.
According to the National Park Service, the restored interior of the house -- listed on the National Register of Historic Places -- still has much of its original detail.
Clinton -- born in Hope on August 19, 1946 -- served in the Oval Office from 1993 to 2001.
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