TMZ Sports has learned there's no official ban on the ultra-popular video game ... it's just become an unspoken rule in the clubhouse that the Sox ain't playin' it until the L's stop piling up.

Of course, Boston's been off to a sluggish start after winning 108 games and the World Series last year ... going just 14-17 in the season's first month.

But, seems they've found a solution to their woes -- put down the controllers ... and start picking up some W's!!!

Star pitcher Nathan Eovaldi spoke with WEEI about the situation, saying, "Maybe if we were doing a little better maybe we would be doing it. But you can’t be losing and playing Fortnite in the clubhouse."

It's a pretty big deal for the guys in Beantown ... the Sox were one of the strongest proponents of the game last year, hittin' popular Fortnite dance moves all over the diamond.

But, don't bet on the game's banishment taking too long ... the Red Sox have won six of their last 10 -- and Mookie Betts is just starting to heat up!!!