Two gunmen surrounded the home for the elderly in Aden while another four fighters entered the building, witnesses and officials said.
They said the gunmen moved from room to room, handcuffing the victims before shooting them in the head.
The officials spoke on condition of anonymity because they were not authorised to speak to the press.
One nun who survived and was rescued by locals said that she hid inside a fridge in a store room after hearing a Yemeni guard shouting "run, run."
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All had been shot in the head and were handcuffed. He said that in addition to the four Indian nuns, six Ethiopians, one Yemeni cook, and Yemeni guards were among those killed.
He said that his family was the first to arrive at the house and that he spoke to the surviving nun, who was crying and shaking. Haidar said that his family later handed her over to southern fighters in charge of security in the local Aden district, Sheikh Osman.
The bodies were transferred to a police station and then a hospital run by the aid organization known as Doctors Without Borders or MSF. An official with MSF confirmed that 15 bodies had arrived at the hospital. Haider said his family took his brother's body for burial.
Aden descended into lawlessness after a Saudi-led coalition recaptured the city from Shiite Houthi rebels last summer.
Yemen's civil war has split the country in two. The northern region, where Shiite rebels are in control, has been struck by an extensive air campaign by a Saudi-led coalition.
The southern region, which is controlled by the internationally-recognized government backed by Saudi Arabia, is suffering from a power and security vacuum.
Al-Qaida controls several southern cities and ISIS group has claimed responsibility for a wave of deadly attacks in Aden, including a suicide bombing that killed the city's governor and several assassination attempts on top officials.
Aden's churches have also come under attack. In the summer, a Catholic church in the district of Crater was torched and sabotaged by Islamic extremists.