"Musharraf is reaping what he had sown," Sharif said.
"I have no personal enmity with Musharraf but he must be taken to task for violating the Constitution of Pakistan," the PML-N chief said.
The Islamabad High Court's order issued yesterday for the arrest of Musharraf over the imposition of emergency rule in 2007 was a "victory for justice", the former premier said.
He said the action taken by the judiciary against Musharraf is a 'reversal of fortunes'.
The PML-N also claimed credit for the court's order, saying the party had thwarted all attempts to give indemnity to the former dictator.
"It's a triumph of justice and a retribution for what the dictator had done during his regime," PML-N president Shahbaz Sharif said.
"Musharraf was first an accused, became a criminal later and now he has become an absconder," PML-N spokesman Pervaiz Rashid said, referring to Musharraf's escape from the Islamabad High Court after the revocation of his bail.
He said Musharraf was now the head of a political party and his previous institution, the army, should have no concern for him.
Musharraf had come to power in 1999 by ousting the PML-N government led by Nawaz Sharif in a bloodless coup.