Culp terminated his campaign committee, according to documents filed with the Minnesota Campaign Finance and Public Disclosure Board. Culp did not return a phone call seeking comment.
Senate District 26 DFL Chairman Mark Liebow said Culp called him to let him know he was dropping out of the race.
"He told me that and then I haven't heard from him since, "Liebow said.
Culp announced his candidacy in October. He is executive director of Lake City's Economic Development Authority.
No other candidates have stepped forward to challenge Nelson in November.