Marine scientist Andrew Wilson, a member of the Whale and Dolphin Research Team at the Environment Society of Oman, told Gulf News he learned of the whales' deaths from fishermen.
Wilson said one of the whales was seen floating dead near the Halaniyat Islands and the other was apparently still alive when it washed ashore in eastern Oman.
"The death of two Arabian sea humpback whales is of great concern, as it represents 2 percent of the estimated population," said Sayyida Tania Al Saeed, the ESO president.
Wilson said fishermen took photographs and recorded video on a mobile phone of the whale that was still alive in Al Qurm, about 31 miles south of Al Ashkharah.
The whale, still moving in the video, "must [have been] breathing its last," he said.
Wilson said his team would conduct more research on the whales and skin samples and photos taken by local fishermen would aid in the research.
The Arabian Sea humpback whales typically breed and remain in the same geographical area, unlike migrating populations of whales.
The humpback whales, Wilson said, sing and males fight by head-butting one another.