The UN ships were set for Indonesia's Aceh province when they were attacked on Sunday, said Noel Choong of the International Maritime Bureau.
The pirates stole some cash and construction materials belonging to the UN's World Food Programme.
The Japanese ship's crew repulsed an attack on Tuesday.
A crew member noticed an unlit speedboat approaching.
"They used high-pressure fire hoses and floodlights on the pirate's boat to scare them off, but the pirates, believed to be armed with guns, still chased them for about five minutes before vanishing," Mr Choong told Kyodo news agency.
No injuries were reported in the incidents, but they raised fears of a resurgence of piracy in the area.
"The attacks took place not far apart from each other. There is a possibility that they were carried out by the same pirates," Mr Choong told reporters on Tuesday.
"We hope the two attacks are isolated incidents and not a start of more attacks," he said.
The Malacca Strait has typically been one of the most pirate-infested sea lanes in the world - and it is also one of the busiest.
Three states bordering the waterway - Malaysia, Indonesia and Singapore - have launched aggressive joint measures to try to cut piracy, including air and naval patrols.
What is your reaction to this story? Have you ever experienced a similar incident on the Malacca Straits? Send us your comments and experiences.
When I was a young man on active service in the east, I was witness to the savagery of these brutes in the Malacca Straits. Our ship was attacked during a night raid by a great gang of them, wielding a variety of implements including guns, knives and chair legs.
Brigadier Charles Arthur-Strong, Tunbridge Wells, UK
I worked recently for an International NGO in Aceh...Piracy is known to be endemic in the Strait, lots of local Govt officials are involved..UN ships are an easy target asunlike most merchantmen, they carry no armed personnel. I am only suprised that this has not happened sooner !
Fraser, Kenya
As a former merchant seafarer I can remember being on a British LPG ship in the southern end of the Malacca Straits in 1985. At about 0700 we were attacked by a high speed launch with some unsavoury-looking characters aboard armed with machetes. We had been forewarned by the authorities and had rigged high pressure hoses all round the ship. Our crew drenched the attackers and they veered off.
John Palethorpe, Leeds England
Until merchant vessels that are scheduled to travel through this area are either escorted through it by naval ships, or allowed to bear arms to defend themselves, these attacks will continue. The misconception of pirates as the pegleg, eyepatch wearing character could not be further from the truth. The modern day pirates arrive on extremely fast launches, which are usually built of fibreglass and are so small that they do not appear on Radar. They are armed with automatic weapons and usually board vessels at night and from the stern.
Nigel Hampson, Burnley, Lancashire
I grew up in the Johor State (the most southern state of Malaysia) and had the unenviable opportunity of getting to know some of these pirates when I was a kid. The pirates I met are mainly of Indonesian descent - fishermen at daytime that turned pirates at night or during low season. Interestingly, they criss-crossed M'sia/Indonesia as though the border never existed and many of them had families and children in both countries too! Despite their fearsome reputation, they do like kids; I remember receiving gifts from them -small fishes, prawns, crabs etc.
ML, M'sia
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According to a maritime regulator, pirates have attacked two UN-contracted ships in the Malacca Strait.

Reports say that no personnel on the ships were harmed, but the pirates took money and building materials belonging to the UN's World Food Programme.

Noel Choong, of the International Maritime Bureau’s piracy centre in Malaysia, said the two ships were sailing from Sumatra to Aceh when the pirates struck. "The attacks took place not far apart from each other. There is a possibility that they were carried out by the same pirates," Mr Choong revealed.

The attacks have boosted fears that piracy is escalating in the area. "We hope the two attacks are isolated incidents and not a start of more attacks," Mr Choong added. 

The Malacca Strait is one of the busiest sea lanes in the world, and for centuries, piracy has been a notorious threat in the Strait.

In 2005, Malaysia, Indonesia, Singapore and Thailand announced they would start air patrols in a bid to tackle the threat from piracy.