The children -- five boys and a girl -- had found the explosive device in a pile of garbage near their home, the Express Tribune reported.
District police officer Iftikhar Ahmed told CNN the children were playing with the grenade when it went off.
The five brothers died immediately and their sister later died at the hospital. One boy was being treated for injuries, though it wasn't clear whether he was related to the children who died, Dawn News reported.
Ahmed said the father of the dead children, Fazl Gul, was being investigated for a possible link to terrorism.
Notable deaths of 2014 [PHOTOS]