Italian news agency ANSA reported the prefecture of Genoa made the decision following widespread clashes between the two clubs' hardcore ultras before and after Wednesday's derby, won 6-5 on penalties by Sampdoria.
A source at Genoa told AFP the club hierarchy was preparing an announcement of its own on the decision.
Samp could also have supporters barred from their next home match, against Juve Stabia in Serie B on October 4, after dozens of injuries to fans and police on a day of tension in the Italian port city.
On Thursday, Italy's interior ministry said its public security department was evaluating Genoa and Samp's next four matches, asking Serie A and Serie B to tell the clubs to not sell tickets for those fixtures until a decision is made.
Genoa head into Saturday's home clash with Juventus one point above the relegation zone.
Wednesday's violence was followed by more disorder between Napoli and Palermo fans on Thursday.
Supporters caused a seven-minute delay to the start of the second half of the match, won 5-0 by Napoli, by throwing flares and firecrackers at each other.
Napoli fans were also involved in clashes with Cagliari fans in Sardinia earlier this month.
