In a petition dated Tuesday, California venture capitalist Michael Goguen accused Brunner of defamation.
The allegations against Goguen, which he denies, are an issue in the Missouri governor's race because Goguen gave $1 million to Republican candidate Eric Greitens.
Brunner in a recent debate said Greitens took money from "the owner of a teenage sex slave."
Brunner's campaign spokesman says the lawsuit is an attempt by a donor of Greitens to distract from other issues in the race.
The other GOP candidates in the Aug. 2 primary are former U.S. Attorney and House Speaker Catherine Hanaway and Lt. Gov. Peter Kinder. They've called on Greitens to return the money.
(Copyright 2016 The Associated Press)