The news was revealed by the website of the Neue Zürcher Zeitung newspaper and was later confirmed to Swiss news agency ATS by a FOJ spokesman.
The account details will be transferred to US authorities as part of their investigation into widespread corruption at world football's governing body which led to 14 officials and sports marketing executives being charged over bribery allegations amounting to more than $150 million.
The account holders can appeal against the FOJ decision in the next 30 days before Switzerland's Federal Criminal Court.
A total of four requests for mutual assistance have been made to the FOJ in relation to the investigation.
No details were released as to the account holders or which banks were concerned.
At the beginning of November, UBS and Credit Suisse, the two biggest banks in Switzerland, revealed they had been questioned by American and Swiss authorities looking into the corruption scandal.
Last month, long-time Fifa president Sepp Blatter was suspended, as was Uefa chief Michel Platini, who has his sights set on Blatter's job but is facing a life ban from football following a request by Fifa's ethics watchdog on Tuesday.
A new Fifa head is set to be elected on February 26th.
The FOJ has already approved the extradition of several FIFA officials to the United States.
Two have already been handed over to American authorities but five others are fighting against the extradition requests.
According to Swiss law, banks are required to report all suspicious accounts and transactions.
In July, Swiss authorities said they had uncovered 81 suspected money laundering transactions linked to the Fifa scandal.
And in September, Switzerland's attorney general Michael Lauber said investigators had seized assets, including apartments in the Alps, and were scrutinizing 121 bank accounts.
“Clearly, we are not even near the half-time break,” he told reporters at the time.