Mr Munter, who reportedly possessed the NoC, was stopped at Benazir Bhutto International Airport, and asked about the document, while he was travelling to Karachi last week. The envoy "strongly protested" the incident, which was subsequently taken up with President Asif Ali Zardari, the Dawn newspaper reported.
The incident reflects the tensions that have characterized Pakistan-US relations in recent since al-Qaeda leader Osama bin Laden was killed by American special forces in a covert raid in Abbottabad on May 2.
Pakistan has threatened to impose "more formal restrictions" where US diplomats will have to provide prior notification before traveling in the country. They however dropped the demand when the US administration threatened similar restrictions for Pakistani diplomats in the US, an unnamed US official was quoted as saying by ABC News.
Pakistan's Inter-Services Intelligence (ISI) has also begun keeping a close watch on American diplomats in the wake of the raid against Bin Laden as it believed the CIA was running a secret network of American and Pakistani operatives in the country.
When contacted the Pakistani Foreign Office sought to play down the incident involving Ambassador Munter. Spokesperson Tehmina Janjua said that "no US-specific" travel restrictions had been applied.
"However, there are general guidelines regarding the travel of Pakistan-based diplomats, designed only to ensure their safety and security, which have existed for a long time," she said in a statement.