Taliban insurgents launched the attacks in the early morning in the Qalai Sang area of the provincial capital Lashkar Gah.
"Our police fought them back, but unfortunately 11 of our police were martyred and two wounded," provincial governor Hayatullah Hayat told AFP, adding that the militants fled after the attack.
Provincial police chief Ghafar Safi said 15 Taliban fighters were also killed during the skirmish.
After 16 years of war the resurgent militants show no signs of fatigue, ramping up their campaign against beleaguered government forces, underscoring rising insecurity in the war-torn country.
Afghan police and troops -- beset by a high death toll, desertions and non-existent "ghost soldiers" on the payroll -- have been struggling to beat back the insurgents since US-led NATO troops ended their combat mission in December 2014.
Also on Sunday, a suicide car bomb attack targeting NATO forces in neighbouring Kandahar province killed at least one woman and wounded four other Afghan civilians, General Abdul Razeq, the provincial police chief, told AFP.
A NATO spokesman in Kabul told AFP they were still checking reports concerning the attack.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)