"Like other players in the past, Ali Mohamed will have to find himself a nickname if he is going to play at Teddy," the hardcore "La Familia" group posted on its Facebook page, which has 36,000 followers.
Beitar, based at Jerusalem's Teddy Stadium, has historically been considered anti-Muslim and anti-Arab.
But despite his name, the 23-year-old striker from Niger is actually Christian, Israeli media reported.
The first division club, which has its roots in the nationalist right, is the only Israeli side never to have fielded an Arab player, although Arabs account for 17.5 percent of the country's population.
In 2013, the club's signing of two Muslim players from Chechnya sparked tension.
Reaction from fans led to the team having to employ bodyguards for them and the club's offices were torched.
In 2017 club manager Eli Cohen resigned under pressure after pledging never to sign a Muslim player.