The highway bridge collapsed last week, claiming 43 lives.
Rather than their usual uniforms, match officials and players from all 20 teams will wear shirts adorned with the message “Genova nel cuore” (Genoa in our heart).
The message will be accompanied by a drawing of a heart joining the two sections of the collapsed bridge.
Serie A organisers have also announced that funding will be allocated to help locals of the Ligurian city recover from the tragic incident.
“I am thankful for this initiative which has great significance for us,” Genoa mayor Marco Bucci said.
“It moves us to feel so much solidarity coming from so many parts. It helps us to go forward with courage and determination, and above all, it is good for the soul of this city.”
Serie A teams held a minute’s silence in remembrance of the Genoa victims before this season’s first round of matches last weekend.
The city’s two main football teams - Sampdoria and Genoa - postponed their opening matches.
