Consul Malik Mohamed Javed went missing after evening prayers on Saturday in the western Amariya district and his family contacted the police, said Pakistan's Charges D'Affaires Muhammad Iftikhar Anjum.
"Persons claiming to be members of Umar bin Khattab group have apparently kidnapped the official," the Pakistani Foreign Ministry said in a statement on Sunday.
Police said Javed had failed to return from prayers at a mosque near his home.
Scores of foreigners have been seized in Iraq over the past year, some by fighters with political demands and others by criminals seeking a ransom.
An Egyptian diplomat was seized by fighters on his way home from prayers last year but was freed a few days later.
Ease security, legislators urge
Meanwhile, Iraqi lawmakers on Sunday called for easing security measures imposed every time they meet, and some legislators complained they were unfairly targeted for searches at Iraqi police checkpoints.
During Sunday's National Assembly meeting, parliament speaker Hajim al-Hasani called for relaxing security measures that have snarled traffic and closed many Baghdad streets when lawmakers meet.
Speaker Hajim al-Hasani says
security is exaggerated
Many residents have complained about the increased security in a city already under tight control. Some lawmakers said they had been insulted and mistreated by Iraqi police at checkpoints.
"These measures are highly exaggerated and they hinder the work of the employees and the movement of the citizens," al-Hasani said. "We asked the security officials to relax these measures."
He said the assembly would officially inform the authorities of their request. "We are keen on guaranteeing the security of the members of the National Assembly, but we are also keen on allowing people to do their jobs," he said.
Qasim Dawud, Iraq's minister of state for national security, said the measures were necessary as long as the assembly continued to convene at the same location.
"Terrorism is targeting the National Assembly ... and that's why we have to focus on security," he said.
Also on Sunday, more than 1000 teachers protested in Sulaimaniya, 260km northeast of Baghdad, demanding that officials update the curriculum and increase teachers' salaries.
"These curriculum are based on political ideas rather than educational ones, so they must be changed," said Sirdar Muhammad, a 39-year-old history teacher.