"We've arrested a computer mastermind. He is linked to al-Qaida. We got information from computer and email," Rashid told reporters on Monday.
Refusing to reveal the computer expert's nationality, the minister said he was captured either in the eastern city of Lahore or nearby industrial town Gujarat.
The capture was around the same time as the arrest of another suspect Ahmad Khalfan Ghailani, Rashid said, but he would not specify the date.
The arrest of Ghailani, which was only announced late on 29 July, also yielded valuable information, the minister said.
Ghailani is wanted in the US for his alleged role in the 1998 bombings of the embassies in Kenya and Tanzania.
Senior US officials told the New York Times and Washington Post that the information found in Pakistan in late July led to the latest "terror alert" in the United States.
The Pakistani officials said documents uncovered in Ghailani's home in Gujarat show specific information on the Citigroup Centre in Manhattan, the World Bank in Washington and other financial institutions, including parking arrangements and whether guards are armed.
The documents also describe the use of phony couriers and delivery people to get inside the buildings to collect information, intelligence officials told the Post.
They said the computer expert, identified as 25-year-old Muhammad Naim Nur Khan, used a "al-Qaida communications system" where information was transferred via "coded messages".
All this "evidence" was urgently relayed to Washington on Friday afternoon and resulted in the US raising terror alert levels on Sunday.