This followed an examination of documents and electronic devices onboard, the police said.
Gibraltar forces and British marines seized the tanker on 4 July off the coast of Gibraltar, saying they believed it to be destined for Syria to deliver oil, in contrast with European sanctions.
Iran denied that the vessel was heading to Syria and condemned the detention.
Laboratory tests confirmed that the tanker was carrying 2.1 million barrels of crude oil, which creates environmental concerns for maintenance of the cargo, a Gibraltar police official said.
The arrests come after London said on Thursday that armed Iranian boats tried to "impede" a UK supertanker in the Gulf before being warned off by a British warship.
Britain said Thursday three Iranian boats had attempted to impede the passage of a British oil tanker in the Gulf, forcing UK warship HMS Montrose to intervene.
These incidents come amid a growing tension between Iran and the West, in light of two different cases of attacks against tankers in the Persian Gulf in May and June, as well as the subsequent shooting down of an American surveillance drone by Iranian forces.