BBC has reported Mr Paty, who was killed on Friday, had earlier shown controversial cartoons of the Prophet Muhammad to his pupils.
The 48-year-old father, who has not been officially named, is accused of issuing a “fatwa” against the teacher.
The brutal murder of Mr Paty, 47, has shocked France.
Tens of thousands of people took part in rallies across France at the weekend to honor him and defend freedom of speech. A silent march was held on Tuesday evening in the suburb north-west of Paris where he was killed.
A man named as 18-year-old Abdoulakh A was shot dead by police after killing Mr Paty on Friday.
The father of the pupil is reported to have exchanged a number of text messages with Mr Paty’s killer prior to the attack close to the teacher’s school in Conflans-Sainte-Honorine.
He is accused, along with a preacher described by French media as a radical Islamist, of calling for Mr Paty to be punished by issuing a so-called “fatwa” (considered a legal ruling by Islamic scholars).
Interior Minister Gérald Darmanin said the two men had been arrested and were being investigated for an “assassination in connection with a terrorist enterprise”.