The insurgents announced the killings on its Andalus radio, saying they were carried out in a public square in Jamame, in Lower Jubba region, late yesterday.
The group said it killed Siyad Ali Abdi, 26, Ahmed Ibrahim, 28, Yusuf Makaran, 58, and Abdullahi Omar, 26, after its court convicted them of assisting drone attacks in Somalia which killed rebel leaders.
Al-Shabab, al-Qaida's East African affiliate, has been fighting for years to impose a strict version of Islam in this Horn of Africa nation.