Government spokesman Gabriel Attal said the Collective Cheikh Yassine group was formally banned during a Cabinet meeting because it was “implicated, linked to Friday’s attack” and was used to promote anti-republican hate speech.
Other groups will be dissolved “in the coming weeks” for similar reasons, he said.
Mr Attal also confirmed the government has ordered a mosque in the north-east Paris suburb of Pantin to close for six months.
A terror investigation is under way into teacher Samuel Paty’s death.
The killer has been identified by authorities as Abdoullakh Anzorov., an 18-year-old Moscow-born Chechen refugee who was later shot dead by police.
A judicial official said seven people who were detained as part of an investigation into the killing, including two minors, will go before an investigating magistrate later on Wednesday for eventual preliminary charges.
The seven are among 16 people, including five adolescents, initially detained for questioning. Nine are being released.
Named after an assassinated leader of the Palestinian Hamas, Collective Cheikh Yassine was founded in the early 2000s by a man who is among the individuals detained for questioning in the teacher’s killing.
Interior Minister Gerald Darmanin said on French news broadcaster BFMTV that the person in question helped disseminate a message that called for mobilisation against the teacher.
The message, prepared by a student’s father, was part of what increasingly appears to be a case turning in part on a spiralling fever on social media among some Muslim individuals or groups.
The Pantin mosque is being punished for relaying the angry father’s message on social media.
The father quoted his 13-year-old daughter as saying the teacher had asked Muslims to leave the classroom – a version that was contested by Mr Paty himself, according to media reports.
Authorities say the mosque has long had an imam following the Salafist path, a rigorous interpretation of the Muslim holy book.
On Tuesday evening, thousands of people gathered to honour Mr Paty where he was beheaded as he left school in Conflans-Sainte-Honorine, north-west of Paris.
A national memorial event is scheduled to be held Wednesday evening in the courtyard of the Sorbonne university.