There was no immediate claim of responsibility but Aden has seen a surge in attacks by the Islamic State group and rival al Qaeda.
Four gunmen entered the refuge operated by Mother Teresa's Missionaries of Charity in Aden's Sheikh Othman district, killing a guard before tying up and shooting employees, security officials told AFP.
Yemen’s Aden governor assassinated
Screams of elderly residents echoed from the home during the shooting rampage, witnesses said.
They recounted seeing the bodies of slain workers with their arms tied behind their backs scattered on the blood-stained floor as the aged residents cried out in fear.
Apart from the four Indians, the rest of those killed were Yemenis working at the facility, officials said.
"I went out for Friday prayers. When I came back, I found all my friends dead," one of the residents said.
It is not the first deady attack on the Mother Teresa order in Yemen.
Drone strike kills four al Qaeda suspects in Yemen
In 1998, three of its nuns were shot dead in western Yemen by a psychiatric patient who had volunteered to fight alongside Bosnian Muslims in 1992 before returning to the Arabian Peninsula country.
The latest attack comes with Yemen's internationally recognised government grappling with an Iran-backed rebellion on one side and a growing extremists presence on the other.
One official said the attackers were "extremists" and blamed the Islamic State group, which has been gaining ground in Aden in recent months.
President Abedrabbo Mansour Hadi has declared Aden to be Yemen's temporary capital as Sanaa remains in the hands of the Huthi rebels and their allies since they seized it in September 2014.
Further east, a suspected drone strike hit a vehicle carrying al Qaeda militants in Shabwa province, killing four, local government and tribal sources said Friday.
Only the United States is known to operate armed drones over Yemen.
Al Qaeda and IS have stepped up attacks in Aden despite the efforts of the government and its backers in a Saudi-led coalition battling the Huthis to secure it.
However, most attacks have so far targeted coalition forces and pro-government Yemeni troops.
Late on Thursday, gunmen in Aden shot dead Hussein al-Wuhayshi, a leader of a local pro-government militia formed in the south in 2011 to fight al Qaeda, along with his brother, a security official said.
On Monday, a suicide car bombing in Sheikh Othman hit a gathering of loyalist forces, killing four people and wounding five others, according to a security official.
The Huthi rebels controlled Yemen's main port city for months before government loyalists pushed them out in July.
Because of the unrest gripping Aden, Hadi and many senior officials in his government spend most of their time in Riyadh.
Al-Qaeda has been well-established for years in south Yemen, but now faces competition from IS, which has mounted a series of deadly attacks, particularly in Aden.
In December, suspected militants blew up a small deserted Catholic church in the city dating from the 1950s when Aden was a British protectorate.
More than 6,000 people have been killed in the Yemeni conflict with more than 80 percent of the population in dire need of food, medicine or other basic necessities, according to the United Nations.
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