The 27-year-old running back was originally given a two-game suspension in July following the incident, which happened back in February this year.
However, the Ravens opted to cut ties with Rice this week after TMZ released CCTV footage of the incident, showing the NFL player knocking out his then-fiancee while in a casino lift.
Mayweather gave his thoughts on Rice's punishment by telling reporters: "They had said that they had suspended him for two games. Whether they saw the tape or not, I truly believe a person should stick to their word.
"If you tell me you're going to do something, do what you say you're going to do. But once again, I'm not in the NFL, so I can't really speak on the situation.
"I think there's a lot worse things that go on in other people's households, also. It's just not caught on video."
Mayweather has been convicted twice for domestic violence and is facing another trial after his ex-fiancee Shantel Jackson filed a lawsuit against the boxer, claiming that he had beaten her and once held a gun to her head.