They say 84 people were wounded in Arad and another 78 in Dimona, after ballistic missiles hit the towns on Saturday evening. BBC reported.
The International Atomic Energy Agency (IAEA) says it is not aware of any damage to the nuclear research facility located about 13km (eight miles) outside Dimona.
Iranian state TV earlier said the strikes were in response to an attack on Iran's Natanz nuclear facility on Saturday.
On Sunday, at least seven people were injured in an Iranian missile attack on Tel Aviv, emergency services say.
The Israeli Air Force says Tehran has fired 400 missiles at Israel since the US-Israeli attack on Iran on 28 February. Of these, 92% were intercepted, it adds.
In Arad, local residents said the blasts they heard on Saturday were terrifying. The missile badly damaged several buildings, leaving a deep crater.
Naram Zaid, a paramedic in the town, told BBC News she had seen a "lot of children with head and chest injuries" after being crushed by objects inside a damaged building.
"I was trying to reassure a 10-year-old girl with head injuries, with blood on her face from broken glass," she added.
"She was refusing to get into the ambulance as her parents were still inside the building, and we waited for her parents to be evacuated from the destroyed apartment block and then we sent them all to hospital."
The outside walls of two residential apartment buildings were gouged out by the impact.
Crowds of dark-suited men stood staring at the damage in this Ultra-Orthodox town in the Negev desert.
