The other detainees include four family members of the killer, a father at the school and a known Islamist radical.
Police carried out some 40 raids on the homes of suspected radicals on Monday and more raids are expected.
The brutal killing has shocked France.
Tens of thousands of people took part in rallies across the country on Sunday to honour Mr Paty and defend freedom of speech. A ceremony paying tribute to Mr Paty, who was 47, will be held at the Sorbonne University in Paris on Wednesday.