Fieger was living in Woodland Hills, Calif., and was being treated for cancer, The Detroit News reported.
"Our hearts are broken, we will miss you Doug," band members said on Knack.com.
The band built a large and influential following in the Los Angeles club scene of the late 1970s and recorded its debut album, Get The Knack, which included My Sharona, in 11 days for $17,000.
Capitol Records pulled out all the stops promoting the album and Rolling Stone magazine referred to the band as "the new Fab Four," a reference to the Beatles.
Billboard named My Sharona the No. 1 single of 1979. The song has been covered by numerous artists and returned to music charts in 1994 after it was included on the soundtrack for the hit movie Reality Bites.
Fieger co-wrote My Sharona with bandmate Berton Averre after being initially rebuffed by a teenage girl of the same name in 1978.
Fieger told People magazine in 1995 he had hoped she would be flattered by such lines as "I always get it up for the touch of the younger kind." She eventually dumped her boyfriend, joined Fieger on tour, graduated from high school and became a rock-star girlfriend for three years.
The woman, Sharona Alperin, has been selling real estate to entertainment industry clients in Los Angeles for over 20 years.