An early trailer release for the film shows Muppet-like characters engaged in sex, coarse language, drugs and violence.
Sesame Workshop alleges in the lawsuit, filed on Thursday in New York state court, that STX Productions has created confusion among the public into believing the film is connected to the show and infringed on the "Sesame Street" trademark.
"As evidenced by a parade of social media posts, emails and public comments, the 'No Sesame. All Street.' tagline has confused and appalled viewers because of what they believe to be a serious breach of trust," the lawsuit alleges.
In response, STX issued a statement in the name of one of the film's characters, the attorney Fred.
"STX loved the idea of working closely with Brian Henson and the Jim Henson Company to tell the untold story of the active lives of Henson puppets when they're not performing in front of children," the statement said.
"While we're disappointed that 'Sesame Street' does not share in the fun, we are confident in our legal position," it added.
The Happytime Murders, scheduled for an Aug. 17 release in the US, is directed by Brian Henson, the son of "The Muppet Show" creator Jim Henson who also helped develop the puppet characters of "Sesame Street" when it launched in 1969.
The film stars comedian Melissa McCarthy as a detective who is tasked with tracking down a serial killer in a world in which puppets and humans coexist.
The lawsuit also asks for punitive damages and a jury trial.