The singer proposed to Brady in Hawaii in 2011 after about five years of dating. He has since been touring with Aerosmith in support of the band's upcoming album "Music From Another Dimension."
"Steven has quietly ended it with his fiancee," an unidentified insider told the Post.
"Steven has been trying to maintain his lifestyle and to stay clean," the source said. "The tour is really important to him and the band. So he decided to end it."
But an Aerosmith publicist shot down the report.
"Just as any couple goes through trials and tribulations in a relationship, Steven and Erin are asking for their privacy at this time," the band's representative told the Post. "They are engaged to be married and each is committed to their sobriety. Any claim to the contrary is absolutely false and misleading."