The officials said the source of the explosion was not clear, but they believe it was either a car bomb or a roadside bomb that was detonated by remote control.
Almost all 33 passengers on the bus were wounded by the explosion and were being treated in hospitals in Egypt and across the border in the Israeli port city of Eilat, said the officials.
They said the bus had arrived at the Taba crossing from the ancient Greek Orthodox monastery of St Catherine's in central Sinai.
