The bombing was followed by gunshots, the officials said, as witnesses said the noise of the blast was huge and that several ambulances rushed to the scene.
The interior ministry gave a casualty toll of one policeman killed and 18 people wounded, including six civilians.
Ismailiya and surrounding areas in the Sinai have seen regular militant attacks on police and military personnel, especially since the military toppled Islamist president Mohamed Morsi on July 3.
The group had also claimed a car bombing in September that targeted the convoy of Egypt's interior minister Mohamed Ibrahim in Cairo. He was not hurt in that attack.
The military has been conducting an extensive operation in the Sinai Peninsula, east of the Suez Canal, to track down Islamist militants.