Jimmy Fallon: NBC Threatens Celebs ... It's Fallon or the Highway

NBC is coming down like a hammer on celebs who want to get on Jimmy Fallon's show ... if they dare do a show on CBS or ABC ... they can forget about "The Tonight Show."

Sources connected to CBS, NBC and ABC tell TMZ ... the Peacock network believes Jimmy Fallon's ratings success gives them extreme bargaining power.  They put the word out to celebs, agents and publicists ... if they want to be on Fallon they can't appear on ANY other network ... and not just shows that go head-to-head with Jimmy, but morning shows as well.

We're told NBC is saying the stars who go on Fallon are also allowed to appear on "Today," "Dateline" and any similar shows they air, but that's it. 

A GMA source says they've already gotten fallout from people they were trying to book.

Fallon is dominating late night .... crushing Jimmy Kimmel by bringing in more than twice the number of viewers.