The unidentified man was transported onboard an Omani military aircraft after his release was secured "following a request by the US government (to Oman) to continue helping in (releasing) its citizens held in Yemen", the ministry said in a statement carried by the state news agency ONA.
It said he was set free following "coordination with concerned parties in Sanaa," in an apparent reference to Iran-backed Shiite Huthi rebels.
Last month, Muscat secured the release of two other Americans who were held in Sanaa.
Since the Huthi rebels overran the capital in September 2014, they have detained several Westerners, most of whom have been released through Omani mediation.
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In September, a US citizen who ran an English-language school in Sanaa was detained by men who said they were security officers working for the Huthis, witnesses said at the time.
A rebel leader later said the US national was detained for providing the Saudi-led coalition with target coordinates for its deadly campaign against the Iran-backed Huthis.
It is the only GCC country not to have joined the coalition air war against the Huthis and their allies in Yemen, although it maintains good relations with regional powerhouse Saudi Arabia.
Oman is also one of the few Arab countries to have a good relationship with Shiite Iran and has mediated between Tehran and Washington on prisoners in the past.
In September last year, Yemeni rebels freed six foreigners, two of them Americans.