The New York rapper described their marriage as "irretrievably broken".
The couple were wed in secret in 2017, and have a two-year-old daughter named Kulture.
Court records obtained by the PA news agency show that Cardi is asking for "primary physical custody" of the child, and wants Offset to contribute for "support and maintenance".
Cardi, 27, whose real name is Belcalis Almanzar, filed for divorce on Tuesday in her husband's home state of Georgia, where the couple have been living.