The charge stems from allegations that Greitens used a photo of his naked mistress as a form of blackmail to keep her quiet about their affair.
Greitens, who was elected governor in 2016, was taken into custody and booked at the St. Louis Justice Center on Thursday afternoon.
The indictment states that on March 21, 2015, Greitens photographed a woman identified only by her initials "in a state of full or partial nudity" without her knowledge or consent.
Greitens is also accused of transmitting the nude photo so that it could be accessed on a computer.
If convicted, Greitens, 43, faces up to four years in prison and/or a $5,000 fine, Ryan said, adding that a judge had ordered Greitens to be released on his own recognizance.
The woman's ex-husband provided an audio recording to KMOV of the woman confessing to the affair and claiming that Greitens threatened to blackmail her. (Greitens has denied he threatened to blackmail her.) Shortly after, St. Louis Circuit Attorney Kim Gardner launched an investigation into the allegations against the governor. A news release from Gardner says it is a felony if a person transmits an image "in a manner that allows access to that image via a computer".
An attorney for the woman with whom Greitens had an affair could not immediately be reached for comment. Greitens' attorney has said allegations of blackmail against the governor were false.
Adam Vinatieri to re-sign with Colts, set for 23rd NFL season
Vinatieri will also most likely break Andersen's record of 2,544 points to become the NFL's all-time scoring leader. He won another Super Bowl in 2006, successfully kicking 14 of 15 field goals on the Colts' four-game playoff run.
"We will carefully examine the facts contained in the indictment and answer the question as to whether or not the governor can lead our state while a felony case moves forward".
Mr Greitens admitted last month he had a relationship with his hairdresser.
"As I have said before, I made a personal mistake before I was governor. My client is absolutely innocent", Dowd said in a statement. "Missourians thought they voted for a person of character and integrity, and instead they got a liar and alleged criminal".
House Minority Leader Gail Beatty (D-Kansas City) said Greitens should consider resigning.
"It will be extremely hard for the governor to effectively do his job with a felony indictment hanging over his head", she said.
State House Republican leaders said an investigation was forthcoming.
The House has the power to initiate impeachment proceedings against a governor. "It's best to let the system take its course".