The Arab Coalition in Yemen said on Tuesday that it had taken an injured crew member from a "suspect" Iranian ship north-west of Hodeidah port after Saudi Arabia received a request from Iran for help.
The coalition, led by Saudi Arabia has been battling the Iran-backed Houthi movement in Yemen for four years.
Coalition spokesman Col Turki Al Malki said the Iranian crew member was flown from the Savis to a military hospital in the Saudi city of Jizan, along the border with Yemen.
The crew member was "subjected to a serious injury and his condition deteriorated on board the ship", which was 95 nautical miles north-west of the Red Sea port.
The cause of injury was not specified.
Col Al Malki said the kingdom had received the request from the charge d'affaires of the Iranian delegation to the UN.
He said the assistance was provided "despite the threat represented by this suspect vessel, the hostile acts it [Iran] carries out against coalition forces and the interests of the Yemeni people, and its continued threats to maritime lanes and global trade on the Red Sea".
Iranian officials were not immediately available for comment.
In early May, Saudi Arabia's coast guard towed an Iranian oil tanker with engine trouble off the coast of Jeddah in the Red Sea.
The Arab Coalition intervened in Yemen in 2015 to try to restore the internationally recognised government of President Abdrabu Mansur Hadi, which was forced from 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.