Wallace has been a vocal supporter of the Black Lives Matter movement, and has used his platform to voice his objections to racism and racial injustice.
"This is a hard time for our sport, but we are going to react swiftly", said Steve Phelps, president of Nascar, during a call with reporters Monday afternoon.
The flag has always been a staple at NASCAR tracks in the sport's southern USA heartlands, but it remains a symbol of slavery and racism for many.
The incident occurred just days after Wallace, NASCAR's only black driver, successfully petitioned officials to ban the Confederate flag from all events and venues.
"Regardless of whether federal charges can be brought, this type of action has no place in our society, " according to the joint statement issued Monday.
Despite NASCAR's ruling, outside the Alabama track on Sunday there were still plenty of Confederate flags flying and merchandise for sale. That would include crew members for each of the 40 teams, NASCAR employees, Talladega staff members and any contracted safety crews or security guards.
Fans were not granted access to the infield or the restricted area of the Cup Series garage.
Even in victory, Ryan Blaney thought about what happened to close friend Bubba Wallace over the weekend. Sunday's race, which was to be NASCAR's first with fans since the coronavirus pandemic erupted, was postponed until Monday by thunderstorms.
A man selling Confederate flags, along with "Trump 2020" banners and other wares near the race site, said they were "doing very well" in terms of customer popularity. "I ask the NASCAR family to rally around Bubba and his team as they compete today, and I know that there are more people who are wishing him well today than ever before". Driver Kevin Harvick then suggested that the drivers should push Wallace's auto to the front of the field. "Supporting you from afar, proud of you".
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