A US embassy spokesperson said the mission had no further details, but had no indication at this point that the death, which follows shootings of German and British nationals here, was related to terrorism.
"The body of an American citizen was found in Al-Hail South, in the governorate of Muscat, on December 31," said an Omani police official quoted by the official ONA news agency.
"All procedures were immediately taken by the investigation teams," the official said without elaborating.
The embassy official said the dead person was "a male American citizen" but could not give any details about his identity or the circumstances of his death.
A German tourist was shot to death in Muscat in early December, in what diplomats said was the second mysterious shooting of a Westerner in about a month.
Another European tourist was shot and seriously injured in Muscat a month earlier. Omani authorities said that incident was a hunting accident.
Oman has strong military and diplomatic ties with the West - mainly Britain - and its society is more tolerant of Westerners than some countries in the mainly conservative, Muslim Gulf region.
The country draws some 650,000 tourists a year with its tropical beaches, as well as ancient courtyards and palaces.
Anti-Western sentiment has been running high in the Middle East since the US-led war on Iraq. Much of the anger has been directed at the United States, which is seen by Arabs as biased towards Israel in its conflict with the Palestinians.