The incident occurred in Kot Rasha Kishan town of Punjab province Tuesday, The Nation reported.
"A responsible state cannot tolerate mob rule and public lynching with impunity," Sharif said.
"I have directed the Punjab chief minister to show no mercy and the law should take its course to punish those who are responsible for this act," the report quoted Sharif as saying.
Police said an enraged mob had beaten a Christian couple to death and burnt their bodies in brick kiln.
Punjab Chief Minister Shahbaz Sharif has ordered a probe and the police have been told to beef up security at in Christian neighbourhoods, an official said.