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.
A man named as 18-year-old Abdoulakh A was shot dead by police on Friday after killing Mr Paty close to his school in Conflans-Sainte-Honorine, a north-west suburb of Paris.
Four school pupils who may have helped identify Mr Paty to his killer in exchange for payment have been detained, a judicial source told the AFP news agency on Monday.
This brings to a total of 15 the number of people taken into custody in the aftermath of the murder.
The killer's grandfather, parents and 17-year-old brother were detained shortly after the gruesome attack.
The father of a pupil who reportedly launched an online campaign against Mr Paty and a preacher described by French media as a radical Islamist were among six people arrested on Saturday. Interior Minister Gérald Darmanin accused the two men of having issued a "fatwa" against the teacher.