Sharks attacked tourists on Tuesday and then again the day after, maiming three Russians and a Ukrainian tourist according to the Russian embassy.
In one of the attacks, an elderly woman lost her hand and another woman lost a leg.
Authorities ordered people to stay out of the waters around Sharm el-Sheikh, a top vacation and diving destination, until the perpetrators were apprehended.
The ministry said it caught a 7 foot (2.25 meter) shark weighing 330 pounds (150 kilograms) and a second that was 8 feet (2.5 meters) long, weighing 550 pounds (250 kilograms) near the resort.
The sharks were taken to Ras Mohammed Conservation Center to be dissected to see if there were any human remains inside.
Mohammed Salem, director of Sinai Conservation, said one of the sharks caught was a Mako shark and the other an Oceanic White Tip, which was the type of shark observed in both attacks.
"Usually these kinds of sharks don't attack human beings but sometimes they have trouble with their nervous system and they accidentally go after people," he told The Associated Press.
He added that Egypt sees one to two fatal shark attacks a year.