The missile appeared to have been fired at the gate of the hotel, they said. A second missile landed nearby, while a third landed in the city’s Buraiqah district, residents said.
Initial reports had described the missiles as rocket-propelled grenades. There was no official word to confirm what type of projectile had been used in the attack.
The Qasr hotel has been the base of Hadi’s government since its gradual return from exile in Riyadh over recent weeks after the expulsion of Iranian-allied Houthi fighters in July.
The hotel has been guarded by troops from the United Arab Emirates, one of the members of a Saudi-led coalition that has been fighting since March to end Houthi control of Yemen and restore Hadi to power in the capital, Sanaa.
The Houthi rebels advanced on the city and in March forced President Abdrabbuh Mansour Hadi and the government to flee to Saudi Arabia.
In July, pro-government militiamen and soldiers drove the Houthis and allied army units loyal to former President Ali Abdullah Saleh out of the port city with the help of coalition ground forces.
Mr Hadi returned to Aden from exile late last month, though he was not reported to be staying at the Hotel Qasr when it was attacked early on Tuesday.
Residents have complained that the city has descended into chaos and lawlessness, with militants affiliated to al-Qaeda and Islamic State seen on the streets.
The UN says almost 4,900 people have been killed in the past six months of fighting in Yemen, including 2,200 civilians.
Northern Shia Muslim rebels known as Houthis, backed by forces loyal to Yemen’s ex-president, took over parts of Yemen, including the capital, Sanaa, and forced the government into exile in March.
The rebels accused the government of corruption and of planning to marginalise their heartland within a proposed federal system.
Forces loyal to the government and Southern militias regained control of Aden in July, aided by Saudi-led coalition air strikes and troops.