Robbiati started his professional career in 1987 with Serie C1 club Monza. In 1993, he signed for Fiorentina, then in Serie B, being instrumental in the "viola"'s successful 1993–94 campaign, which saw them win the Serie B title and obtain promotion to Serie A. He stayed at Fiorentina until 1999; despite often not being featured in the starting lineup, in 1996 he won the Coppa Italia and the Supercoppa Italiana, and he also achieved some success even at the continental level, scoring the decisive goal in the return leg of the UEFA Cup Winners' Cup Round of 16 fixture against Sparta Prague. Fiorentina were ultimately defeated by the eventual champions Barcelona FC in the semi-finals of the tournament. After a season with Napoli, in 2001 Robbiati signed for Inter, but never managed to play a single match with the "nerazzurri", being loaned first to Perugia and then to Fiorentina.