DETROIT — A vacant Detroit housing project that was home to the Supremes before the talented trio struck gold with Motown is coming down.

Demolition of the massive Frederick Douglass Homes — known to most Detroit residents as the Brewster projects — could begin in early 2013, Mayor Dave Bing announced Thursday.

Covering several city blocks, the complex bathes part of downtown and surrounding neighborhoods in shadow and fear and is a symbol of the city’s decline.

A $6.5 million federal Housing and Urban Development grant will cover the cost of tearing down the 75 condo-style apartments, two 6-story buildings, and four 14-story towers. Soil remediation — the removal of any below-ground pollution — is included in that tally.

‘‘It’s going to take us, probably, the better part of a year to get everything down,’’ the mayor told reporters at a news conference in front of the hulking complex. ‘‘This total area will be cleaned up.’’

The city has no set plans for redevelopment of the complex.