EXCLUSIVE

The Patriots were BLINDSIDED by LeGarrette Blount's sudden rise to superstardom -- at least the official team shop was, 'cause they're all SOLD OUT of his jerseys ... and now the team is scrambling to crank out #29s before the next playoff game.

With Blount going bonkers -- scoring 8 TD's in his last 3 games and becoming the first player in NFL history to put up +150 yds and 4 TD's in a single playoff game -- his jersey is becoming impossible to find.

We spoke to several shops in the Boston area, including the official Patriots team store ... and the story was the same everywhere -- WE'RE ALL SOLD OUT OF #29.

Makes sense, since Blount started the season as a backup running back ... but now, the official Pats team shop tells TMZ Sports, they''re literally printing up Blount jerseys one-by-one at the stadium to try to keep up with the demand.

"The Patriots ProShop is one of the few stores around licensed to make customized Nike jerseys," a rep tells us.