The name of the worker has not yet been released.
Mr Sumet said the worker was a male from Pua district of Nan.
The man was injured by a mortar shell fired from the Gaza Strip which hit a house in the Ashkelon Coast Regional Council, the Jarusalem Post reported.
He was rushed to a medical centre in Ashkelon by helicopter where he succumbed to his injuries, it added.
"We feel deep sadness by the death of the migrant worker. We were prepared for the possibility that there would be loss of life. We send our condolences to the victim's family and continue to give our backing to the IDF and the security forces," the newspaper quoted chief of the council Yair Farjoun as saying.