Gen. Ahmed Bakr, head of security in the North Sinai, said the couple and the guide were kidnapped when Bedouins stopped a tour bus en route to Taba, CNN reported.
EgyNews reported the three people who were kidnapped remain in the area where they had been abducted.
The kidnappers want authorities to release a relative detained in Alexandria on drug charges, Bakr said.
Security sources "confirmed that continuous efforts are being made in order to determine the whereabouts of the Americans and the Egyptian tour guide on one hand, and to release them in coordination with tribal leaders and the families in the region," EgyNews said.
CNN said the number of kidnappings and robberies in Egypt has increased since last year's ouster of dictator Hosni Mubarak.
Two American tourists were kidnapped and quickly released in the Sinai region in February. In June, two American tourists kidnapped in the region were released a day after they were abducted.
In a message posted on Twitter Friday, the U.S. Embassy in Cairo said it was "in close touch with Egyptian authorities, who are doing everything they can to bring about safe release of the American tourists."