It is common on matchdays for supporters to park in those areas due to the limited space in the club car park and the location of the ground.
The club will maximise space in the official car park at Glanford Park though, introducing new spaces.
Traffic wardens will also be employed on matchdays to give tickets to any vehicle parked illegally.
Road safety chiefs said they are worried fans attending games could become involved in a serious accident.
"It's a large road with a national speed limit and one of our officers saw people with kids walking down the side of the road while lorries were passing," Humberside Police's football liaison officer PC Alan Welsh told the Scunthorpe Telegraph.
"We weren't happy about people doing that because the risk is so high so the council and ourselves looked at the problem and decided double yellow lines were the only way to go."
Iron Supporters Club chairman Andy Brown added: "I know those roads are freeways and people shouldn't be parking there, but where are they supposed to park?
"The old Scunthorpe council encouraged the club to go outside the town boundaries and now it's difficult to get there without a car.
"Perhaps they could get people to park at the old Tesco car park, at Skippingdale, and provide free buses for park-and-ride.
"It's a difficult situation, and I wish they had approached us before making this decision."