The case involves a former state employee, Mike Duncan, who says he was fired for political reasons.
Governor Fletcher was served the subpoena by the Jefferson County Sheriff's Department on Friday.
Attorneys for Duncan say they want Fletcher as a possible witness because they say he was involved in Duncan's firing in 2005.
Duncan worked as the top investigator for the Transportation Cabinet's Office of Inspector General.
He says he was fired because he is a Democrat.
The hearing is on Wednesday.