A source at the network, who spoke on the condition of anonymity because the person was not allowed to discuss the matter publicly, said the producer was suspended after a remark about 2-year-old Blue Ivy's hair.
On Monday's show during a segment about Blue Ivy's hypothetical thoughts during Sunday's MTV Video Music Awards, guest host Karrueche Tran said: "I really did wake up like this, because my parents never comb my hair." Blue Ivy joined her mother onstage at the VMAs.
Stephen Hill, BET's president of music programming and specials, publicly apologized on Twitter.
"Last night on 106 & Park there was a stupid, unthoughtful joke made about a young child," Hill tweeted.
Hill also said the network privately apologized to Beyonce and Jay Z.
BET didn't immediately return an email seeking comment Wednesday.
Tran, who has dated singer Chris Brown on and off, tweeted Tuesday that she did not write the joke. She wrote: "Now y'all know I LOVE me some Beyonce and Blue Ivy!"
Hill also tweeted that it was not Tran's fault.
"We also apologize to her for putting her in that position," he wrote.