Gov. Eric Greitens of Missouri was indicted on Thursday on a felony invasion of privacy charge, threatening his hold on the leadership of the state and creating chaos across Missouri’s political landscape in an election year.

The St. Louis grand jury’s indictment accused Mr. Greitens, a first-term Republican who was seen as having ambitions for higher office, of photographing a nude or partially nude person without the person’s knowledge or consent in 2015. The indictment said Mr. Greitens then transmitted the photo in a way that allowed it to be viewed on a computer, which prosecutors said made the crime a felony rather than a misdemeanor.

The charge comes weeks after Mr. Greitens acknowledged having an extramarital affair in 2015, but denied reports that he blackmailed the woman or took a nude photo of her without permission. A St. Louis television station had aired a report with claims that Mr. Greitens, a married father of two, took a compromising photograph of a woman with whom he was having an affair and then threatened her with retribution if she revealed the relationship.

Mr. Greitens, a former Navy SEAL and Rhodes scholar who has been governor for just over a year, has resisted calls to resign, insisting that he did nothing illegal. He has been touring the state touting his tax cut plans.