Bishop Yves Boivineau had warned Fr Vesin about his “active membership” of the Grand Orient de France lodge.
Freemasonry has been condemned as anti-Christian and anti-clerical by various popes through history.
Bishop Boivineau ordered the priest to cease his functions “at Rome’s request”, the parish said.
In March, the Vatican’s Congregation for the Doctrine of the Faith – effectively the Church’s watchdog – asked for the priest’s departure.
Three members of the diocese of Annecy then met him but Fr Vesin said he would not leave the lodge.
A statement from the diocese quoted by Le Figaro newspaper stressed that the penalty imposed on the Freemason priest was not final and could yet be lifted because “mercy goes hand in hand with truth”.
BBC News – Vatican punishes French priest for being a Freemason
Bad Vatican 