Cardi B addressed an unnamed person in the post, explaining she has tried to settle their differences calmly and privately in the past, but couldn't restrain herself Friday.
"When you mention my child, you choose to like comments about me as a mother, make comments about my abilities to take care of my daughter is when all bets are (expletive) off!!" Cardi B wrote. "I've worked to hard and come too far to let anyone (expletive) with my success!!!!"
People.com said Cardi B, 25, was seen wearing a torn dress and lunging at 35-year-old Minaj, who had her back against a wall and was surrounded by security guards at the Harper's Bazaar ICONS party.
Witnesses said Cardi B at some point threw her shoe at Minaj.
Cardi B was barefoot and had a welt on her head when she was escorted out of the event. It was unclear how she sustained the injury.
Minaj posted photos on Instagram of herself looking glamorous at the event, but she did not say anything about the altercation.
Both women have albums on the Billboard 200 chart this week -- Minaj's Queen is No. 5 and Cardi B's Invasion of Privacy is No. 10.
Cardi B gave birth on July 10 to her first child with her husband, Migos rapper Offset. The couple named their daughter Kulture Kiari Cephus.