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The shooting happened Friday evening in Baton Rouge. The East Baton Rouge Sheriff's Office said 34-year-old Lynzell Anderson remained in jail Saturday.
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Anderson was grabbing his keys inside his Baton Rouge home, preparing to drive to the store with his son and fiancée, when he heard a gunshot from the driveway, according to a probable cause form provided by the East Baton Rouge Sheriff's Office.
It was not immediately clear whether he has an attorney. Baton Rouge Mayor Sharon Weston Broome says the child's death is "equally sad and frustrating."
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Broome asks people to pray for the family. She also says free gun locks are available at Baton Rouge City Hall.
Anderson told investigators that he typically stores a gun underneath the passenger seat, unprotected.
The Associated Press contributed to this report.