An FBI spokesman said the money was in $100 bills, adding that it was unclear when the money was stolen, according to an online report from CNN.
After the plane landed on Saturday, the money was found missing on Monday from a container used by banks to transfer currency, which was loaded into a larger cargo container.
A law enforcement source told CNN the cash belonged to an American bank that was transferring the money from offices in Switzerland to the US.
According to another police source, the money was headed for a Federal Reserve facility in Rutherford, New Jersey, where old bills would be exchanged for new ones, before being transferred to the bank somewhere in the US, the online report indicated.
The money was noticed missing when the shipment was delivered to the Federal Reserve facility on Monday the source said, CNN reported.
Speculation is now mounting that the money may well have been stolen in Zurich before the Swiss plane, an Airbus A330-300, took off.
The New York Post, which first broke the story, cited a source saying the exterior cargo container showed no signs of being compromised.
Investigators, including those from the New York Port Authority, were examining wether local mechanics, flight-crew members or other airport personnel got inside the inner container to steal the money, the newspaper reported.
Whoever took the cash wouldn’t have much trouble carrying it, the Post said, noting that $1 million in $100 bills weighs about 22 pounds (10 kilograms), according to the US Treasury.