Darryl "DMC" McDaniels said that products sold by Amazon, Walmart and other stores violated federal trademark and New York competition laws.
McDaniels, who owns a firm named Run-DMC Brand, made the allegations in a complaint filed in the US District Court in Manhattan.
The products include T-shirts and hats.
Run-DMC were one of the biggest rap acts of the 1980s, with global chart hits including Walk This Way and It's Tricky.
Their distinctive logo has become a fashionable motif on T-shirts, often worn by people who are not necessarily fans of the group's music.
McDaniels said the brand was "extremely valuable" and had been legitimately licensed to various manufacturers including sportswear firm Adidas, itself the subject of one of Run-DMC's most successful songs.
Amazon and Walmart have yet to comment on the lawsuit.
McDaniels founded the group in 1981 in the New York borough of Queens with fellow rapper Joseph "Run" Simmons, who is now an ordained Pentecostal minister known as Reverend Run.
The third original member of the group, DJ Jam Master Jay, was shot dead by an unknown assailant in a recording studio in Queens in 2002.
A member of pioneering rap group Run-DMC has filed a $50m (Â£40.7m) lawsuit accusing retailers of unlawfully using the group's name on items of clothing.