The blast went off at around 11.30am (0930 GMT) on Monday at the Hasharon shopping centre in the upmarket resort town of Netanya which has been the scene of several previous bombings claimed by Palestinian resistance movements.
Police told public radio that four people were known to have died in the blast while sources with the Magen David Adom ambulance service said that 35 people had been wounded in the attack.
It was not immediately clear if the toll included the suspected bomber.
Aljazeera's correspondent in Palestine said no group had claimed responsibility so far despite reports of claims by Palestinian resistance groups.
Speaking to Aljazeera on Monday, Khidr Habib, an Islamic Jihad spokesman from Gaza, said the group neither rejected nor claimed responsibility for the bombing.
The Palestinian Authority has condemned the attack.