The special prosecutor, who would most likely be based in another Missouri county, would have 27 days from Monday to re-file the charges before the statute of limitations expires, according to the Kansas City Star.
The committee is expected to issue its final report during the upcoming special session, which could recommend impeaching Greitens.
Still, the collapse of the case may not revive Greitens' political standing.
Missouri Gov. Eric Greitens is calling the decision to drop a criminal charge against him "a great victory that has been a longtime coming".
Prosecutors cited a decision by the judge to allow Greitens' attorneys to call Circuit Attorney Kim Gardner as a witness. They accused them of perjury and withholding evidence on April 12. I am extraordinarily grateful for the tremendous patience and courage of friends, family, and people of faith, who have all recognized that in time comes the truth.
But the St. Louis circuit attorney's office says it still plans to pursue the case, either through a special prosecutor or an appointed assistant.
"Today, the prosecutor dropped the false charges against me".
Jury selection began on Thursday. Defense lawyers alleged the investigator committed perjury when he said he didn't take notes during the interview.
Greitens was accused of taking and transmitting a nonconsensual photo of an at least partially nude woman with whom he had an affair in 2015.
Gardner's spokeswoman, Susan Ryan, noted that the charge could also be re-filed as a misdemeanor, which would not require providing that the photo was made available via computer.
The case was suddenly dismissed after both sides went into Circuit Judge Rex Burlison's chambers, following the meeting - a spokesman for the circuit attorney said the charges will be refiled with special prosecutor. "The court's order places the Circuit Attorney in the impossible position of being a witness, subject to cross-examination within the offer of proof by her own subordinates".
Sullivan cited the fact that Greitens' defense attorneys planned to call the St. Louis circuit attorney, whose handling of the case has been under constant criticism by Greitens attorneys.
Searches of the governor's smartphone and Apple cloud data found no evidence of the image, and no witness, including Greitens' ex-lover, has ever seen it.
On Monday morning, Missouri Gov. Eric Greitens sat in a St. Louis courtroom watching potential jurors answer questions about allegations that he attempted to blackmail his one-time lover. But his attorneys have been trying to exclude those who may have difficulty setting aside their opinions.