The move was introduced for players at the Blue Square Bet Premier club a few weeks ago but now the policy has been extended to the whole stadium.
The Gloucestershire club is owned by Dale Vince who is a vegan who runs green electricity company Ecotricity.
Free-range poultry and fish from sustainable stocks will continue to be served.
Communications director Tom Williams said: "Following discussions with the manager and on nutritional advice, it was decided to no longer feed our team red meat for health and performance reasons.
"[It has now been] decided that this policy should be extended to the stadium, at least in part as a further step in establishing ourselves as a "green" organisation.
"We appreciate some will miss their burgers and sausages, but our catering staff are working hard on a range of tasty and interesting products to replace those that are no longer available.
"This is obviously a break with tradition but in time we hope that many will come to see it as a step forward rather than a step backwards.
"We're a country now where apparently chicken tikka masala is the most popular national dish. I think the old sausage bap won't be much lamented."
Mr Vince added that "if red meat was not good enough to feed our players, then it wasn't good enough for our staff, fans and visitors too".
He said: "At its worst it means once every two weeks watching a football game without being able to eat red meat.
"Anybody that really needs it can bring a ham sandwich or something if they wish - that's no problem."
Tim Barnard, who is chairman of Forest Green Rovers' Supporters Trust, said: "There were a few raised eyebrows on Saturday when there was no cottage pie.
"But I'm a traditional chips and curry sauce man myself so it doesn't really affect me."
A spokeswoman for the Vegetarian Society said: "A diet lower in meat, particularly red meat, and higher in plant-based food is lower in fat, higher in fibre and higher in trace minerals.
"Anything the British population as a whole can do to reduce their reliance on meat has got to be positive."
Burgers and sausages have been banned from being sold to fans at Forest Green Rovers football club.