The Playpen site was located on the Tor network which is used to anonymise web-browsing activity.
The FBI found a way around this to reveal the users' real IP addresses and led to 200 prosecutions.
But it refused to reveal to the court how it managed the feat.
The site was located on the Tor network which many people use to browse the web anonymously. It conceals their location and identity by routing their connections through a chain of different computers and encrypting data in the process.
To get round this the FBI used what it called "network investigative techniques" and revealed people's identities.
But it refused a request for information on its technological investigation techniques.
Federal prosecutor Annette Hayes wrote in a court filing on Friday that "because the government remains unwilling to disclose certain discovery related to the FBI's deployment of a 'network investigative technique'" it was "deprived of the evidence needed to establish defendant Jay Michaud's guilt beyond reasonable doubt".
The government's Motion to Dismiss order is pending before the court and the judge is expected to sign a dismissal order "within the next day or two", the assistant public defender Colin Fieman told the BBC.
Mr Michaud's case is one of many emerging from the investigation into Playpen users.
In December, the Assistant Attorney General Leslie Caldwell said the investigation of Playpen led to more than 200 active prosecutions and the identification or rescue of at least 49 American children who were subject to sexual abuse.
In January, Michael Fluckiger was sentenced to 20 years in jail for running the Playpen site.
Once the site's administrators had been arrested, the FBI kept the site going for 13 days to gather information about members.
US prosecutors have dropped a case against a man accused of using a child porn site because the government refused to divulge how it revealed his identity.