Hassan Nouripour, the chairman of Sadaf Sefid Khark diving company, was quoted by the ISNA as saying on Tuesday: "Twelve divers who were working in international waters were arrested by United Arab Emirates forces".
Nouripour said that the diving firm had sent its employees out to the ship after the vessel's owner asked the company to retrieve the cargo from the sea floor and had received full permission from the Iranian authorities.
It had apparently sunk last year while sailing from Dubai to the port of Dailam in southern Iran when caught out by a sudden storm.
"The ship was some 22 nautical miles away from the UAE in international waters but Tuesday last week two Emirati patrol boats came to the site, talked to our divers and forcefully took them to the UAE."
UAE authorities were not immediately available for comment.
The foreign ministry official told ISNA: "These divers were 18 miles off Abu Musa and 24 nautical miles away from the UAE. Therefore their arrest was completely illegal."
"To solve the issue we are pursuing it and it resulted into our embassy staff meeting them.
"Currently these 12 divers are in a good condition and we are following their case to release them."
The islands were seized by Iran after British forces left the Gulf region in 1971 but are claimed by the UAE.
Disputes over the islands have on occasion strained relations between the two countries who nonetheless maintain robust links, especially in trade.
The maritime dispute also sparked the 2005 arrest and imprisonment by Iran of a Frenchman and a German who strayed into territorial Iranian waters after navigating on the basis of maps handed out in the UAE.
After spending more than a year in Iranian jails they were pardoned and released.
In March, Iranian naval forces seized 15 British sailors and marines in the Gulf, claiming they had entered Iran's territorial waters. Britain countered that they had been engaged in anti-smuggling operations in Iraqi waters.
The 14 men and one woman were freed after two weeks in captivity.