"An 18-month-old baby was killed in a strike east of Bureij (refugee) camp in central Gaza," spokesman Adham Abu Selmiya said, naming the toddler as Iyyad Abu Khusa.
Health ministry spokesman Ashraf al-Qudra said that the two wounded boys, aged four and five, were "in critical condition."
The Israeli military had no immediate comment on the strike, which took place several hours after two other people were killed in separate air strikes on the northern towns of Beit Hanun and Beit Lahiya.
The attacks came after a quiet night on the Israeli side of the border, with the military confirming that no rockets had hit between 9:00 pm (1900 GMT yesterday) and 7:00 am (0500 GMT) today, after which two struck the south.
The latest air strikes raised the death toll in Gaza from Israeli air strikes since Wednesday to 47, with more than 450 people wounded, the emergency services said.