ExxonMobil Exploration & Production Malaysia will use the two vessels - Icon Zara and Icon Ikhlas - to transport supplies between supply bases and drilling rigs or platforms.
The contract is worth 7.7 million ringgit ($1.8 million), according to a securities filing.
The six-month contract for Icon Zara started on 30 September, with an option for a one-month extension.
Icon Ikhlas, on a three-month charter, started work for ExxonMobil on 1 October.
