The 26-year-old model hosted BET's 106 & Park on Monday, and joked about Beyoncé and Jay Z's daughter's appearance at the 2014 MTV Video Music Awards during the episode.
"I really did wake up like this, because my parents never comb my hair," she said in an imitation of the two-year-old.
Beyoncé fans immediately began harassing Tran on social media, but the remark was reportedly part of the script and not the model's own doing. Tran released an apology through her publicist Tuesday, and said there was a script change shortly before showtime to include coverage of the VMAs.
"I am a huge Beyoncé fan and I love Blue Ivy," she declared in the statement. "I apologize for the comment and wish I had a chance to review the revised script so that I could have avoided participating in that segment."
"I never expected things to turn out this way," she added on Instagram. "I apologize to any and everyone who felt offended in any way by the comments made by BET executed through me. I would never disrespect anyone's child in any way and anyone who knows me knows that I LOVE Beyonce."
BET music programming president Stephen Hill has corroborated Tran's story, and apologized for the comment himself on Twitter.
"Last night on 106 & Park there was a stupid, unthoughtful joke made about a young child," he acknowledged. "We apologize publicly to the child's parents (and have done so privately) and we have taken punitive actions with those responsible ... Oh, and please don't hate on Karrueche; it was NOT her fault. We also apologize for putting her in that position."