A spokesman for Thomas Cook, which has customers in Hurghada, said: "Thomas Cook is aware of a knife attack that has taken place on the beach in Hurghada in Egypt".
The attacker in Hurghada stabbed the tourists in the face, neck and feet, according to the security official.
The two women who have died are believed to be Ukrainian but no further details have been released.
The attack came as gunmen ambushed an Egyptian security checkpoint yesterday, opening fire on a auto and killing five policemen in an area just south of the capital, the state-run MENA news agency and the Interior Ministry said.
The nationalities of the injured women were not clear immediately, it said. The statement said that the man was being questioned and that the ministry has beefed up security in the area to ensure the safety of tourists.
"A police officer who was near the site of the attack exchanged fire with the assailants forcing them to flee", the statement said.
"We don't know his motives yet, he could be insane or perturbed - it's too early to tell", a senior interior ministry official told AFP.More news: ATM Spits Out Desperate Note From Trapped Man
A security official at the El Palacio hotel told Reuters two of the injured were Czech and two Armenian, but other officials said one of the women was Russian.
Hurghada is a popular Egyptian holiday resort.
Insurgents have carried out a number of attacks in Egypt since the 2013 military ouster of an elected Islamist president.
The interior ministry also announced early this week the killing of six militants in Southern Egypt as security forces faced militants in gunfire exchange.
"These are insane people", said Tamer Wajeeh, whose tour operator business Red Sea Reisen is about 3km from the scene of the first attack.
The assault in the Red Sea resort of Hurghada came hours after a shooting near famous pyramids outside Cairo killed five policemen. He said police arrived to the crime scene in "just a few minutes".