Four gunmen stormed the facility in Aden's Sheikh Othman district, killing a guard before tying up and shooting employees, the officials told AFP.
Dozens of stricken family members arrived at the site following the attack, witnesses said.
One official said the attackers were "extremists" and blamed the Islamic State group, which has been gaining ground in Aden in recent months.
The dead nurses were Indian nuns, the officials said, adding that the rest of those killed were Yemenis working at the home.
No group claimed responsibility for Friday's attack, the first of its kind in Yemen, where the internationally-recognised government is grappling with an Iran-backed rebellion on one side and a growing jihadist presence on the other.
President Abedrabbo Mansour Hadi has declared Aden 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 all four on board, 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 and their allies to secure it.
However, most of the jihadists' attacks have targeted coalition forces and pro-government Yemeni troops.
Late on Thursday, gunmen in Aden shot dead Hussein al-Wuhayshi, a leader of local pro-government militia formed in the south in 2011 to fight Al-Qaeda, along with his brother, a security official said.
On Monday, suicide car bombing in Sheikh Othman hit a gathering of loyalist forces killing four people and wounding five others, according to a security official.
A suicide bombing last month in Aden claimed by IS killed 14 soldiers.
The rebels controlled Yemen's main port city for months before government loyalists pushed them out in July.
Because of the unrest gripping Aden, Hadi himself 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 jihadists blew up a small deserted Catholic church in Aden, completely destroying the building which was attached to a cemetery and built in 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.
