"By connection, Assab in Eritrea has also been affected because it was a staging ground for our operations in Hodeidah", the official said, adding that troop movements in other areas of Yemen are "tactical and based on our needs".
The agency quoted the official as saying the UAE was moving from "military first strategy to a peace first strategy".
The Yemeni official said the UAE has trained tens of thousands of Yemenis to fight against jihadists from Al-Qaeda in the Arabian Peninsula and the Islamic State group in southern provinces - mainly Aden, Mukalla and Shabwa.
The drawdown "was not a last-minute decision" and had been discussed extensively with Riyadh, said the official, who declined to be named. The long-delayed redeployment of Houthi forces there is seen as a key first step toward ending the civil war, which erupted in 2014 when the Houthis seized the capital, Sanaa.
Diplomats have said the UAE prefers to have forces and equipment on hand should tensions between the United States and Iran escalate further after attacks on oil tankers in the Gulf and Tehran's downing of a U.S. unmanned drone.
The UAE announcement comes amid a standoff between the United States and Iran, which spiked in June when Iran shot down a USA drone following a series of tanker attacks.
The UAE has participated since 2015 in the Saudi-led Arab coalition against insurgent Houthi rebels, considered allies with Iran.
People stand amidst the ruins of a Yemen building destroyed during past Saudi-led coalition air strikes.
Civilians have borne the brunt of the conflict, which has created what the United Nations says is the world's worst humanitarian crisis.
The UAE supports US sanctions on Iran, but has also stressed that war with Iran is not in the region's interest.