SPA said the "Happiness 1" vessel was found 70 kilometres southwest of Jeddah Islamic Port and the captain had requested a tow due to "engine failure and loss of control".
Its crew of 24 Iranians and two Bangladeshis were unharmed.
The request for assistance was made by Iran through the Saudi delegation to the United Nations in New York.
Riyadh broke ties with Tehran in 2016 after Iranian protesters set fire to Saudi Arabia's diplomatic mission in response to their execution of a prominent Saudi Shia cleric.
"The kingdom received an official request for help, through its permanent delegation to the United Nations in New York, from the Iranian charge d'affaires in the Iranian delegation," SPA quoted a coastguard spokesman as saying.
"All necessary precautions were taken for the safety of the crew and to ensure there is no environmental damage and to provide assistance."
Iran and Saudi Arabia have a long history as adversaries in regional conflicts across the Middle East. They both backed opposing sides in the ongoing unrest in Yemen and Syria.
On Wednesday, Iranian Foreign Minister, Javad Zarif, gestured towards the possibility of starting a dialogue with the kingdom.
"We hope to have the same type of relations with Saudi Arabia, Bahrain and the United Arab Emirates."