"At the moment, there is nothing that would indicate criminal actions", Darmanin said, speaking at the National Assembly.
The minister noted that the investigation was still underway.
"The man who was detained [as part of the investigation] was released ... This [fire] may have an accidental origin", Darmanin added.
Police released a 39-year-old migrant who worked as a volunteer at the cathedral on Monday. He was in charge of locking the building.
The Saturday fire completely destroyed a 400-year-old organ at the cathedral, but the building itself remains intact and is not at risk of collapsing.