Iran and Saudi Arabia are arch-adversaries in the Middle East, backing opposite sides in several regional wars including in Yemen where a Saudi-led coalition has been battling the Iran-aligned Houthi movement for four years.
But Saudi Arabia in June said it had evacuated a crew member for medical reasons from a "suspect" Iranian ship northwest of Hodeidah after receiving a request for help from Tehran.
The Iranian had now been sent to Oman at Tehran's request after receiving the necessary medical treatment in Saudi Arabia, a source in Saudi Arabia's foreign ministry was quoted as saying by state news agency SPA.
"The ministry received a request from the Iranian foreign ministry through the Swiss embassy in Riyadh to transfer (the crew member) to the Sultanate of Oman after his health improved," the Saudi foreign ministry source was quoted as saying by SPA.
Oman traditionally seeks to play a conciliatory role in the turbulent region.
The crew member had been airlifted from the Iranian vessel Savis to a military hospital in the Saudi city of Jizan, which borders Yemen, after being seriously injured on board the ship.
A Western-backed Saudi-led coalition intervened in Yemen in 2015 to try to restore the internationally recognized government of Abd-Rabbu Mansour Hadi which was ousted from power in the capital Sanaa by the Houthis in late 2014.Saudi Arabia accuses Iran of supplying the Houthis with weapons, including drones and missiles that have been launched at Saudi cities. The group and Tehran deny the charges.