Quazi Mohammad Rezwanul Ahsan Nafis, 21, of Bangladesh, travelled to the US with the intent of planning a terrorist attack, the FBI said.
Mr Nafis was arrested after he allegedly attempted to detonate what he thought was a 1,000lb (454kg) bomb.
There was never a threat, the FBI said, as Mr Nafis had been closely watched.
Mr Nafis is charged with attempting to use a weapon of mass destruction and attempting to provide material support to al-Qaeda.
He entered no plea when brought before a federal court on Wednesday.
Mr Nafis travelled to the US in January 2012 and sought out contacts to help him with the attack, officials said in a complaint filed in New Yorkon Wednesday.
One of the people he contacted turned out to be a source working for the FBI, US federal prosecutors said.
Mr Nafis was placed under surveillance, and the undercover FBI agent sold him 20 bags of what he said were 50lb of explosives. The suspect then bought and assembled detonators and timing devices.
Officials said there had never been any actual threat.
The arrest is the latest in a series of so-called “sting” operations run by the FBI and anti-terror authorities in the US.
“We have to be vigilant and I can assure you we’re going to remain vigilant,” New York police commissioner Ray Kelly told reporters, adding the city had not seen a successful attack in 11 years.
Mr Kelly said that Mr Nafis had entered the US on a student visa by purporting to be a college student in Missouri. He also said he had been at least partly motivated by an English-language al-Qaeda magazine called Inspire.
The head of the NYPD said the incident was likely to put the Federal Reserve building on the police department’s list of “iconic targets”.
The building, housing the US central banking organisation, is located in downtown Manhattan in New York City, just a few blocks from the World Trade Center complex in the city’s financial district.
Federal officials say Mr Nafis proposed several targets, including a high-ranking US official and the New York Stock Exchange.
In a statement intended to claim responsibility for the would-be attack, he allegedly said he believed the most efficient way of destroying America was to target the US economy.
Prior to the attempt, Mr Nafis allegedly recorded a video in which he said “We will not stop until we attain victory or martyrdom”, according to the complaint against him.
“The defendant thought he was striking a blow to the American economy. He thought he was directing confederates and fellow believers,” Loretta Lynch, US Attorney for the eastern district of New York said in a statement.
“At every turn, he was wrong, and his extensive efforts to strike at the heart of the nation’s financial system were foiled by effective law enforcement.”
The Bangladeshi, who was living in Queens, New York, reportedly told undercover FBI officials that he had overseas connections to al-Qaeda.