Both Genoa clubs had requested that their opening games of the season be pushed back with Sampdoria due to host Fiorentina and Genoa playing at AC Milan on Sunday.
"The President of the Lega Serie A, given the requests for postponement of their matches scheduled for Sunday, August 19 at 20.30 on the part of the clubs Sampdoria and Genoa as result of the tragedy which hit Genoa, and having received the assent of both Fiorentina and Milan, has decided on the postponement of the Sampdoria-Fiorentina and Milan-Genoa matches," Lega Serie A said in a statement.
"The rescheduled dates for the two matches will be announced in the coming days, in compliance with the regulations in force."
At least 38 people were killed and dozens injured when the Morandi bridge collapsed on Tuesday sending about 35 cars and several trucks plunging 45 metres (150 feet) on to railway tracks below.
Desperate efforts are still underway to find survivors.