The Palestinian group Islamic Jihad said one their men carried out the attack.
Witnesses say they saw a man trying to get into the cafe. When security guards started asking questions, he set off the bomb strapped to his body.
Alert
Israeli officials say they have been on high alert since the start of the war in Iraq.
Many Iraqis support Palestinians.
Security in the area had also been tightened up because it was Land Day.
It's a yearly day of protests by Israeli Arabs to remember land they lost in the 1948 Middle East War.
Sunday's explosion was the first attack like this in Israel since a suicide bombing on 5 March killed 17 people on a bus in Haifa.
Netanya is no stranger to suicide attacks. In March last year, a suicide bomber hit the Park Hotel during Passover, killing 29.
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