At least three Saudi ships are heading through the strait, Bloomberg reports, and AFP says a French tanker has also passed through.
Opening the strait would also allow for an increased flow of oil, particularly from Saudi Arabia, the United Arab Emirates and Iraq.
Iran closed the strait in response to the US and Israeli attacks on the country at the end of February. The US has also responded by blocking Iranian ports in the area.
Several shipping companies are awaiting clearer approval to begin transits - including Stena and Maersk.
