The attacks are believed to be the latest in the Iranian-backed rebels' campaign that has disrupted the $US1 trillion ($A1.5 trillion) in goods that pass through the Red Sea each year over the Israel-Hamas war in the Gaza Strip and has halted some aid shipments to conflict-ravaged Sudan and Yemen.
The new attacks on oil tankers also come amid efforts to salvage the still-burning Sounion oil tanker earlier hit by the Houthis, seeking to head off the potential ecological disaster posed by its cargo of one million barrels of crude oil.
In Monday's first assault, two ballistic missiles hit the oil tanker Blue Lagoon I and a third exploded near the ship, the multi-nation Joint Maritime Information Center overseen by the US Navy said.
"All crew on board are safe (no injury reported)," the centre said.
"The vessel sustained minimal damage but does not require assistance."
Houthi military spokesman Brigadier General Yahya Saree claimed responsibility for the attack on the Blue Lagoon I.
The Blue Lagoon I is travelling south through the Red Sea to an unlisted destination.
The vessel was coming from Russia's port of Ust-Luga on the Baltic Sea and had been broadcasting that it had Russian-origin cargo on board.
The Joint Maritime Information Center said it assessed that the ship "was targeted due to other vessels within its company structure making recent port calls in Israel".
Saree also cited that as the reason the Houthis attacked the vessel.
The British military's United Kingdom Maritime Trade Operations centre reported a second attack off the Houthi-controlled port city of Hodeida.
The private security firm Ambrey said an aerial drone hit a merchant ship, though no damage or injuries were reported.
The attack happened only a few kilometres from where the Blue Lagoon I attack occurred, Ambrey said.
The US military's Central Command, which oversees American operations in the Mideast, identified the second vessel as the Saudi-flagged oil tanker Amjad and blamed the attack on the Houthis.
The Amjad carried two million barrels of oil, it said.
"These reckless acts of terrorism by the Houthis continue to destabilise regional and global commerce, as well as put the lives of civilian mariners and maritime ecosystems at risk," Central Command said.
The Houthi group did not immediately claim responsibility for the second attack.
However, it can take the rebels hours or even days to acknowledge their assaults.
The Houthis have targeted more than 80 vessels with missiles and drones since the war in Gaza started in October.
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