Honey Boo Boo -- TLC Ultimatum to Family ... Stop Pitching Yourselves, Or Else

Honey Boo Boo's hopes of being a pop diva may have just been shattered ... the star's former network says they'll come down on her like a ton of bricks if she releases a song.

Sources close to the family say TLC sent the family an ultimatum ... they can't work for another entertainment company until their contract with the network runs its course at the end of May.

Mama June, Honey, and the fam were in town last week shopping a reboot of their show to other networks and HBB recorded a song, "Movin' Up," with Pumpkin and Adam Barta, produced by LA On The Track.

Our sources say the network would ultimately take them to court if the family tries to make money before June. TLC has paid the entire family their money for the season that never aired, plus tutoring and health insurance.