Iranian patrol boats surrounded a US cargo ship in the strait on Friday.
Earlier this week, Iranian naval ships reportedly fired warning shots near a Marshall Islands-flagged cargo ship before seizing it and its crew.
The strait connects the Arabian Sea and the Persian Gulf.
The US navy will not be escorting the ships - a different procedure from accompanying them. Instead, it will monitor the area as the ships pass across the strait.
The crew of the Marshall Islands-flagged container ship seized by Iran in the strait on Tuesday are safe and "in good spirits", Danish shipping company Maersk said.
Maersk said it still did not know the reason why the Marshall Islands-flagged vessel was seized, and noted it had been in an international shipping lane.
Iranian media cited an official as saying the ship was seized based on a court order in connection with a complaint made by a private Iranian company about debts.
The crew includes a British national, but no Americans, as initial reports suggested.
The narrow strait lies partly in Iranian waters.
Shipping traffic is allowed to pass through under an internationally-recognised protocol called "innocent passage", so long as the ships are not carrying weapons, collecting intelligence, or violating other restrictions.
Defence officials have said that US Navy ships will accompany US-flagged commercial vessels through the Strait of Hormuz, to make sure they are not interfered with by Iran.