He faces a maximum sentence of life in prison if convicted.
Also on Tuesday, Somali pirates freed a chemical tanker and its 23 Filipino crew members after holding them hostage for more than five months.
The ship had reportedly been carrying a cargo of phosphoric acid from Dakar, Senegal, and was en route to Kandla in India when it was seized.
It is not clear if a ransom was paid.
Muse, who was brought to New York by US authorities on Monday night, at one point cried out and appeared to wipe away a tear during the hearing.
|Concerns over piracy in the shipping lanes
off the Horn of Africa have grown [EPA]
His hand remained bandaged after he was hit by a Maersk Alabama crew member armed with a pickaxe as they battled the alleged pirates.
When told by the judge he would be represented by lawyers free of charge, he said through a Somali translator: "I understand. I don't have any money."
Concerns have been raised among the Somali community in North America over the decision to try Muse in the US.
"A teenager coming from a country where there is no law, no government, is suddenly put through one of the highest levels of the criminal justice system in the United States. So this is as confusing as anyone can imagine," Omar Jamal, the executive director of the Somali Justice Advocacy Centre, told Al Jazeera.
The hostage charges relate to the pirates seizing Richard Phillips, the US captain of the Maersk Alabama, and holding him hostage in a small lifeboat.
Phillips was later rescued by US forces after navy snipers shot dead three of the pirates and arrested Muse, allegedly as he was negotiating over the captain's release on a US vessel.
Teenage defendants are entitled to greater protections under international law, and Muse's age could be a factor in a prison sentence if he is convicted.
Plea to Obama
Muse's mother said on Tuesday that he had been coerced into piracy by "gangsters with money" and appealed to Barack Obama, the US president, to release him or to allow her to visit where he is being held.
"I appeal to the American government, President Obama, to release my young, poor misled 16-year-old student son. I appeal for his release. If not, I ask him to take me to where he will be tried," Adar Abdirahman Hassan, who lives in the Somali town of Galkayo, told the Associated Press news agency.
The boy's father, Abdiqadir Muse, also said the pirates had lied to his son, telling him they were going to get money.
The hijacking of the Maersk Alabama prompted calls for tightened measures to protect ships in the busy shipping lanes off the Horn of Africa.