The Brazilian's first season in charge of the club started in encouraging fashion with respective 3-0 and 6-0 wins over Monaco and Angers in Ligue 1.
However, Lyon has failed to win a league match since, its only victory coming in a surprise 2-0 UEFA Champions League defeat of RB Leipzig in Germany on Thursday (AEST).
Sylvinho has paid the price for their dip in form, despite having only taken the job in May.
Lyon confirmed assistant coach Gerald Baticle will take temporary charge of the first team, which lost 1-0 to rival Saint-Etienne on Monday.
Sporting director Juninho Pernambucano, whose future has also come under scrutiny in recent weeks, remains in his role.
Club president Jean-Michel Aulas was quoted by L'Equipe on Monday as saying: "We have rarely been in that situation. Juninho will have to think. We are not where we wanted to be, that's for sure."
Lyon hosts Dijon on 20 October after the international break.