The men were detained on possible charges of "human trafficking and involuntary manslaughter." One of them is the owner of the vessel.
Hundreds of migrants are feared dead after Wednesday's sinking, with just 163 people rescued and 51 bodies recovered, according to the country's military and state media.
The boat had set off from Egypt and was heading for Italy when it was found 12 nautical miles northeast of the town of Rashid -- also known as Rosetta -- in El Beheira Governorate on Wednesday afternoon.
State media said the boat had a maximum capacity of 150 people, but 450 had been crammed aboard. Smugglers were charging 35,000 Egyptian pounds ($3,951) for an Egyptian and $3,000 for foreigners to make the dangerous journey from Egypt to Europe, state media said.
Mahmoud Aly spent Wednesday going between hospitals along the coast. His brother and cousin were on the boat.
He told CNN his cousin was rescued but his 24-year-old brother is missing. "The boat had more people than it could take. It's a wooden boat," he said.
He said his family would spend the night on the beach waiting for boats to resume the search and rescue efforts at daylight. "We saw the last boat after sunset. Seven people were on board."
Hope for survivors dwindling
"Only dead bodies came out of the sea today, no survivors," Mohamed Abu Arab, a Rashid-based fishermen, told CNN.
Meanwhile Mohamed Nasrawy, whose brother was on the boat, spent the night and the early hours of Thursday on the beach looking for his sibling.
At least three families who have been searching for loved ones said so far it had mainly been local fisherman involved in the rescue mission.
'This is a disaster'
Arab told CNN that he and other fisherman are used to finding three, four or five bodies from failed migrant crossing attempts.
"But we haven't seen this before," he said of the number of bodies from the latest incident. "This is a disaster."
Fishermen were the first to spot the capsized boat Wednesday, Arab said, and have been assisting the coast guard in the search for survivors. "Everyone is helping. All security agencies are involved."
Most of the survivors he has seen were Egyptian, he said, but he believes there were also people from Sudan and Somalia.
Week of arrests
The Egyptian military has regularly announced efforts to combat illegal immigration. On the same day the boat capsized, the coast guard foiled an illegal immigration attempt, rescuing 294 on board a boat off the shore of El-Alamein, according to a military statement.
A day earlier, the Egyptian military arrested 68 people on a boat trying to make its way to Europe. They were captured off the coast of Matrouh.
Last week, the country's navy thwarted two attempts by people trying to cross from Egypt to Europe. More than 400 would-be migrants of various nationalities were arrested in that operation.
A perilous journey
Migrants are leaving African countries in large numbers for Europe
, often in overcrowded, rickety boats. The perilous voyages often turn fatal.
Many of the refugees using the central Mediterranean route -- which runs roughly from Libya or other north African countries to Italy -- are from Nigeria, Eritrea and Gambia, according to the International Organization for Migration.
This year, over 300,000 have arrived in Europe by sea, landing mostly in Greece and Italy, according to UN estimates
. Almost 30% are children.
Of those attempting the crossing, 3,211 people are believed to have died at sea, added the report.