Ramadan began in most parts of the country on Friday.
More than 170 people have been hanged in Pakistan since December, prompting criticism from human rights organisations.
Mr Sharif notified the Interior Ministry and provincial governments of the month-long suspension on Thursday.
Pakistan is believed to have the largest number of death row inmates in the world. Some 8,200 prisoners are awaiting execution - many of whom have been in jail for over a decade.
A seven-year moratorium on the death penalty was lifted late last year in response to a deadly Taliban attack on a school in Peshawar.
Amnesty International said it had seen "a conveyor belt of executions" since then.
At least 15 people were put to death earlier this week, in jails across the country. The majority had been convicted of murder and spent many years on death row.