The police say the suicide bomber was a woman who blew herself up when she was challenged by a security guard.
At least 19 people were hurt and three people, including the bomber, killed in the blast inside the SuperSol supermarket, at the shopping mall in the Kiryat Yovel neighbourhood of Jerusalem.
Eye witnesses described scenes of carnage in which much of the large supermarket was destroyed.
Force of blast
One shopper said: "The blast was huge. She (the bomber) was a few metres from the entrance inside".
Another witness, Hanna Cohen, said she was about to enter the store when there was "was a huge blast, and I saw people flying all around, arms and legs"
One man, who arrived just after the blast, described what he saw in an interview with Israel Radio.
"I got there two minutes afterwards. It was a horrible scene," he said, having given his name as Moshe.
He said two dead bodies were at the entrance, apparently those of the bomber and a guard who tried to stop her.
"I understood that the guard did not let the terrorist in, and they were blown up together," he said.
In the aftermath of the attack as medical teams tried to help the injured and police began to seal of the area, a man sat on the steps outside the shopping centre, crying and hugging two small children.