He joined in April to replace the previous chief executive Andy Chen.
"We are thankful to Peter for stepping in as interim CEO," the company said in a statement.
The service, which re-launched in March this year, is hoping to compete with the likes of Spotify, Deezer and Google Play.
Tidal said that "current executives in New York and Oslo will continue to lead our rapidly developing innovation and content initiatives until our new CEO is in place".
Jay Z bought Tidal when he acquired the Swedish company, Aspiro, earlier this year, for $56m (Â£37m).
Artists including Beyonce, Madonna and Alicia Keys also have equity stakes in Tidal.
The project is meant to be more artist-friendly than its rivals - with musicians earnings 75% royalties, compared to Spotify's 70% and Apple's 71%.
However, it has a subscriber base of just 770,000, compared with Spotify's 20 million.
Peter Tonstad, the boss of the Jay Z's music streaming service Tidal, has left the company after just three months in the job.