The plane landed at JFK International Airport on Saturday but on Monday officials noted the disappearance of $1.2 million in $100 bills.
It was part of a larger shipment of $93 million sent by a US bank from its offices in Switzerland to the Federal Reserve in New Jersey, according to ABC News.
Conflicting accounts have emerged about what happened.
ABC news reported that an employee of JFK airport discovered that a box containing the cash was damaged.
“Three crates of cash were delivered to JFK,” ABC News quoted one official saying.
A seal on one of the crates, transported in a larger shipping container, was broken on Monday, the official said.
A forklift operator “opened the sealed crate and noticed damage to one of the crates in the form of a puncture from a forklift. It was a hole large enough to put your arm in.”
The FBI has not yet stated whether the theft occurred in New York or in Zurich.
The online site of Swiss newspaper Blick said American authorities have asked Zurich police for help in the investigation.