The arrests were made from the Lak Pass area of Quetta earlier this week when the three were trying to flee to Afghanistan, intensifying the probe to identify the insiders involved in the attack.
The three were shifted to Karachi for investigation, an official said.
Security forces had killed two militants and arrested another four when they attacked the key warship and submarine repair facility on Saturday.
A navy official said that the interrogation of the arrested militants had provided clues for further arrests and raids.
The recently announced South Asia wing of al-Qaeda also claimed that the dockyard attack was its handiwork.
The group also said that it received help from officials who had deserted the armed forces.
Al-Qaeda chief Ayman Al-Zawahiri last week announced the group's new branch to focus on South Asia and appointed Maulana Asim Umar, a Punjabi militant, as its chief.
Al-Qaeda also said that the group had planned to strike the US fleet in the nearby region after taking over the ship PNS Zulfiqar at the naval dockyard in Karachi.
However, the veracity of the claim could not be independently verified.
A retired security official said that the idea of taking over a naval warship and using its arsenal was "far-fetched".
"The militants are trying to make tall claims to impress their audience. In reality it is not possible because they couldn't even penetrate the dockyard, so how could they take over a ship," he said on condition of anonymity.
At least six militants aided by some Pakistan Navy personnel tried to storm the dockyard last Saturday but the attempt was foiled by marine and army commandos who killed two militants, including a former navy officer who had left the service a few months ago, and captured four others.
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