Smith celebrated the release in a post Friday on Instagram.
"VULGAR is a song that is very special to me. Me, the QUEEN, and a group of some of the most talented people I know, got in the studio the day after the Grammys and we created this piece of music. The creativity was pure and the energy was alive. I'm so excited to share this with you sailors!! VULGAR iS BEAUTIFUL!! Out everywhere now. Love you @madonna."
Madonna posted a video of herself celebrating the song's release with a dance party.
In February, Madonna introduced Smith and Kim Petras ahead of their performance of "Unholy" at the Grammys. Smith and Petras won Best Pop Duo/Group Performance for the song.
"Vulgar" is Smith's first new music since their third studio album, Gloria, released in January.
Madonna released her 14th studio album, Madame X, in 2019, and the compilation album Finally Enough Love: 50 Number Ones in August.
In late May, Smith was forced to cut a show short and cancel concerts due to a vocal cord injury.