People were said to be vomiting and suffering dehydration after an iftar meal, to break the daily Ramadan fast.
The camp, between Mosul and Irbil, houses people displaced by an Iraqi offensive to capture the city of Mosul from so-called Islamic State (IS).
IS fighters are currently under heavy siege in the west of the city.
The Kurdish Rudaw news agency reported that more than 750 cases had been recorded and at least one child had died.
The food was prepared in a restaurant in Irbil and brought to the camp by a Qatari charity, it added.
People were being treated in three hospitals in the area.
The camp is one of 13 built by the UNHCR in the Mosul area to cope with people fleeing from the city and surrounding villages.