Holden Matthews, a 21-year-old white man, faces three counts of simple arson of a religious building.
St Landry parish sheriff Bobby Guidroz said the father of the suspect is a sheriff's deputy in his department.
At a news conference, Mr Guidroz disputed reports that Matthews's father turned his son in.
Mr Guidroz also said the suspect's father knew nothing of his son's alleged involvement in the fires.
The first fire torched the St Mary Baptist Church in Port Barre last month.
Days later, the Greater Union Baptist Church and Mount Pleasant Baptist Church in Opelousas were burned.
Each was more than 100 years old, with mostly black congregations.
The churches were empty at the time of the fires, and no-one was injured.
Louisiana governor John Bel Edwards said federal investigators were looking into whether hate motivated the fires, which he called "evil acts".
