The warning comes a week after a breakaway Taliban faction attacked a northwestern university and killed 21 people, mostly students.
That school - the Bacha Khan University in the northwestern town of Charsadda - reopened briefly yesterday but then closed indefinitely to give students more time to recover from the incident.
The government memo, which was obtained by The Associated Press, says there is intelligence that 13 Taliban fighters recently entered the country from neighboring Afghanistan and were planning suicide attacks on schools across Pakistan.
The schools in Punjab would remain closed till the end of the month, said the province's education minister, Rana Mashood Ahmad.
He did not cite the alert but said the closures were due to harsh winter weather and heavy fog. Schools were also closed in southwestern Baluchistan province for the usual winter break there.
In the northwest and the south, schools remained open and it was not immediately clear if there where additional concerns that prompted the closures in Punjab.
The Charsadda attack revived memories of the horrific December 2014 Taliban attack on an army run school in the nearby city of Peshawar that killed 150 people, 144 of them children.