The state constitution lays out an order of succession in which Lt. Gov. Mike Parson, who was elected separately, will take over for his fellow Republican.
State lawmakers had convened in a special session to hear evidence about Greitens in a process that could have led to his impeachment.
A Cole County judge ruled against Greitens on Tuesday by allowing subpoenas issued by lawmakers investigating the governor to go forward. The legislative investigation had requested numerous documents from Greitens political campaign and from A New Missouri, Inc., the secretive nonprofit formed by his campaign aides to advocate for his agenda.
Greitens was charged with a invasion of privacy felony in February, but that charge temporarily has been dropped. A second felony charge of computer tampering is still pending.