Pakistan's interior minister said the men were "facilitators" in the attack, which left 141 people dead, including 132 children.
Chaudhry Nisar Ali Khan added that intelligence indicated another attack was in the planning.
The Pakistani Taliban says it attacked the military-run school.
All seven attackers were reportedly killed. The Taliban said the raid was in revenge for an army offensive in the north-western region near the border with Afghanistan.
After the attack, the country lifted a moratorium on its use of the death penalty and has since executed six men.
Mr Khan said: "We are receiving intelligence from across the country that the militants are getting ready for another savage and inhuman counter-attack."
He said that he could not yet divulge the number or identity of the men.
Thousands of Pakistanis visited the army-run school on Sunday to mourn those killed.
Pakistan executed four convicts in Faisalabad on Sunday. They were the second set of prisoners to face the death penalty since the lifting of the moratorium.
The four men were convicted of involvement in a plot to assassinate then President Pervez Musharraf in 2003.
One of those executed, Akhlas Akhlaq, had dual Pakistani-Russian citizenship.
Three other men were identified by Pakistan's media as Ghulam Sarwar, Zubair Ahmed and Rashid Tipu.
Two men were also executed on Friday.
Pakistan imposed a de facto death penalty moratorium in 2008.
The new executions come despite calls by the UN not to resume them.
Police in Pakistan say they have arrested several people suspected of involvement in last week's Peshawar school massacre.