Kidnappers boarded a tour bus and abducted Michel Louis, a pastor from Dorchester, Mass.; Lisa Alphonse, a woman from a nearby congregation; and their Egyptian tour guide Friday.
Michel Louis' wife was on the bus at the time, but was not kidnapped.
"Everything happened at once. It was all of a sudden. Even now seems like a dream to her -- a nightmare," Jean Louis, the couple's son, told CNN.
"If we were aware, I would believe we would use correct judgment not to enter that area," Jean Louis said.
EgyNews said the captives remain in the area where they had been abducted.
The kidnappers want authorities to release a relative detained in Alexandria on drug charges, said Gen. Ahmed Bakr, head of security in the North Sinai.
"We understand that it's a little bit different from the normal cases," Jean Louis said. "Because they're not asking for money, it makes it a little more complicated."
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."