The 44-year-old musician was earlier married to pop sensation Jennifer Lopez for eight years and has five children, reported Sun Online.
"The pair got serious very quickly and had the blessing of her parents, but it hasn't worked out," said a source.
The couple raised eyebrows when they got together in February due to their 22-year-old age gap.
Green, 21, is just three years older than Anthony's oldest daughter Ariana - from his relationship with Debbie Rosado.
"It seems to be Marc's decision to end it. She's already moved her stuff from his house in Miami and has gone away with friends to get over it. Things happened very quickly between them - and she'd spent a lot of time with his children," the source added.