The storm -- the second strongest ever recorded in the Arabian Sea -- is expected to make landfall on Yemen's central coast Tuesday.
Chapala was already dumping light to medium rain in Al Mukalla, where wave heights swelled between 1-4 meters (3-13 feet). The storm was some 117 kilometers (72 miles) south of the port city early Tuesday local time.
Chapala was packing maximum sustained winds of 195 kph (120 mph) Monday, but was expected to weaken somewhat as it gets closer to the dry air of the Arabian Peninsula.
The storm is still forecast to pack a punch when it hits Yemen with the strength of a Category 1 hurricane. The major concern is the extraordinary volume of rain it's going to dump on the country's dry, rugged terrain.
The deluge is likely to cause "massive debris flows and flash flooding," CNN meteorologist Tom Sater warned.
Yemen isn't typically in the line of fire for tropical cyclones.
Most of the storms that brew in the Indian Ocean end up in the Bay of Bengal, on the eastern side of the Indian subcontinent. Those that do make their way across the Arabian Sea are more likely to hit Oman, which lies to the north and east of Yemen.
Chapala already brushed past Socotra, a Yemeni island in the Arabian Sea where 60,000 to 65,000 people live.
Abdul-Jamil Mohammed, deputy director of the Environmental Protection Authority on the island, reported strong winds, heavy rain and big waves overnight into Monday.
Mohammed said the storm damaged some homes and uprooted trees in Hadibo, the capital of Socotra. Contact has been lost with the northeastern part of the island since Sunday night, and floods have covered the roads leading there, he said.
"Our problem is we have no one to help us here," he said, explaining the island has one hospital and four ambulances.
Yemen is already dealing with one of the largest humanitarian crises in the world, according to the United Nations.
The country has been plunged into chaos this year by a conflict between Houthi rebels
and forces loyal to deposed President Abdu Rabu Mansour Hadi. A Saudi-led coalition in March began bombing the Houthis, who are aligned with Iran.
The widespread fighting has killed thousands of people, many of them civilians, and left millions more desperately short of food, water and medical supplies, the United Nations says.