The rock drummer's publicist said in a statement Tuesday that the ceremony was part of a double wedding Friday in the backyard of White's musical partner, Jack White.
Smith is the son of punk singer Patti Smith and the late guitarist Fred "Sonic" Smith of the rock band MC5. The younger Smith is also a rock guitarist.
The other couple that wed Friday was Jack Lawrence and his girlfriend Jo McCaughey.
Jack Lawrence is the bass player in Jack White's other musical projects: the Raconteurs and the Dead Weather.
The wedding was attended by a small party of close friends and relatives.
The White Stripes got their start in Detroit. Though Meg and Jack White have claimed to be siblings, court records have suggested they were married for four years before divorcing in 2000.
Meg White and Jackson Smith live in Detroit.
