Calls for Mr Muscat to step down grew after the probe into the 2017 auto bomb killing of anti-corruption journalist Daphne Caruana Galizia led to charges on Saturday against a prominent businessman with alleged ties to ministers and senior officials.
Three men have been in jail as the alleged bombers, but no trial date for them has been set.
Magistrate Audrey Demicoli asked Fenech to enter pleas. He replied that he was pleading not guilty, and he was remanded in custody.
Caruana Galizia wrote about 17 Black less than a year before her death, linking its operation with Schembri and Mizzi. Yorgen Fenech, one of Malta's richest men, was brought in under police guard.
Mr Muscat, in power since 2013, has said he will speak after the investigative case is complete.
Muscat had called the snap legislative elections called after his close entourage was accused of corruption by journalist Daphne Caruana Galizia.
Immediately after Fenech was charged, the family of Caruana Galizia issued a statement saying: "We now expect the Prime Minister to leave office, and parliament, with immediate effect to allow a free and full investigation into his and (former chief of staff) Keith Schembri's role in Daphne's assassination".More news: Martin Scorsese on why series format wasnt ideal for The Irishman
The prime minister has previously said he will only step down when those who ordered the killing are identified. Schembri was questioned by police but ultimately released as they said they did not have enough evidence to hold him. Schembri has denied any wrongdoing.
Speaking yesterday for the first time since his arrest, he denied being the author of a type-written letter that Mr Fenech told police he secretly received after his arrest.
Aged 53, she was known for investigating high-level corruption, including contributing to the 2016 Panama Papers data leak.
A year ago he was identified as the owner of a Dubai-registered company called 17 Black, which is listed in the Panama Papers, a collection of leaked confidential documents showing how wealthy and powerful companies around the world use tax havens to get around the law.
She never discovered who owned the company.
Schembri, a close friend of Muscat's, and former Tourism Minister Konrad Mizzi both resigned on Tuesday.
Schembri has said that 17 Black had been a potential client for his business group.More news: Kanye West features his wife, children in 'Closed on Sunday' visuals
Caruana Galizia was murdered in a vehicle bomb in Malta in October 2017. Last November, an investigation by Reuters https://www.reuters.com/article/us-malta-daphne-offshore-exclusive/exclusive-mystery-company-named-by-murdered-maltese-journalist-is-linked-to-power-station-developer-idUSKCN1NE18M and the Times of Malta showed that 17 Black was owned by Fenech.
Fenech had not commented publicly on this accusation.
Earlier in the week, senior European Union lawmakers announced an urgent mission to Malta to look into the state of the rule of law there amid questions about the independence of the island nation's justice system.
Investigators, who included members of the Federal Bureau of Investigation and Europol, subsequently told a court that the bomb was set off from a yacht off Valletta harbor.
Police sources have called Fenech the chief suspect in the case.
A photograph of Keith Schembri with alleged go-between in the murder Melvin Theuma was published on Saturday by Malta Today, another local news outlet.
It was unclear when the photo was taken.More news: Hillsborough stadium disaster: Police Commander not guilty of manslaughter