The two brothers were arrested in northern Sinai and are believed to be affiliated to a group with radical Islamist views, named by Egypt as Tawhid wal Jihad (One God and Jihad).
The security official said on Saturday initial investigations showed that there were more than 40 other associates of the group who were still on the run.
Twenty people were killed, including several foreigners, on April 24, when three suicide bombings ripped through the popular Red Sea resort of Dahab during a peak holiday season.
About 70 people were also killed in multiple bombings against the resort of Sharm el-Sheikh in July last year and another 34 people died in attacks further up the Red Sea coast in October 2004.
Authorities have blamed Tawhid wal Jihad for the bomb attacks. The group has never issued a statement or claimed responsibility for attacks.
On Friday, an interior ministry statement said police had killed three men wanted for involvement in the Dahab bombings.
The deaths took the total number of suspects killed by police to 10, according to previous interior ministry statements.
Two of the men, Atwan al-Swerki and Radi al-Swerki, were the brothers of Atallah al-Swerki, who is believed to have carried out the Dahab attacks, a security source said on Friday.
The three had been hiding in farms in northern Sinai when police got a tip-off and surrounded the area for hours.
“[The suspects] started to shoot, and police returned fire killing all three instantly,” the source said.