The number of injured people stands at 83, the source added.
Three suicide attackers staged the deadly bombing in Kandahar on Friday, while the fourth opened fire at the worshippers.
SITE Intelligence Group, a security firm researching terror groups, shared a statement attributed to Islamic State-Khorasan (banned in Russia), in which the Islamist group said it was behind what it called a double suicide bombing.
This was the second deadly attack by an affiliated Daesh* terrorist group (banned in Russia) on a Shia mosque in more than a week. A suicide bombing of a packed mosque in the northern Kunduz province killed more than 60 last Friday.