U.S. embassy spokesman Alberto Rodriguez said no Americans were killed or seriously wounded in the attack, which killed one Pakistani and wounded 10 people. He said initial reports suggested it was carried out by a suicide bomber on a motorcycle.
The attack took place on a main road in an area where many Western diplomats live and involved 50 kg (110 pounds) of explosives, police said. "There was an attack on a two-car convoy from the consulate in Peshawar. One car was hit. We are still investigating what actually happened," said Rodriguez.
It was the first attack on Westerners since bin Laden's death.
Peshawar has seen many operations by Taliban militants seeking to topple the U.S.-backed Pakistani government and was home to bin Laden in the 1980s when Islamists were fighting the Soviet occupation of Afghanistan.
Al Qaeda and its ally, the Pakistani Taliban, have vowed to avenge the killing of bin Laden by U.S. special forces on May 2, and, the group said it would target the Pakistani government and its Western allies.
"The diplomatic staff of all NATO countries are our targets," said Ehsanullah Ehsan, a Taliban spokesman, told Reuters via telephone from an undisclosed location.
"We will continue such attacks. Pakistan is our first target, and America is our second."
Peshawar police chief Liaqat Ali told reporters a booby-trapped car appeared to have been parked at the side of the road and exploded as one consulate vehicle was near.
Many Pakistanis are frustrated with the inability of security forces to subdue the Taliban. In a separate attack on Friday, an explosion killed five people and wounded four in the tribal region of Orakzai in the northwest, officials said.
"The security after the killing of Osama has been lax instead of being tighter. We are feeling insecure," said Tahir Khan, 20, a student standing near the site of the blast in Peshawar.
One of the consulate vehicles, which police said was armored, was riddled with shrapnel. The blast forced it to slam into an electricity pole beside a pre-school.
"I had just arrived at school and was about to start my work when there was a big blast. The windows of our school were broken and I was hurt," said school administrator Zahid Zaman from a hospital bed.
Police superintendent Ijaz Khan told Reuters two American security guards were slightly wounded, and were being treated at a U.S. medical facility.
Americans have been targeted before in Pakistan.
In April of 2010, militants using a car bomb and firing weapons attacked the U.S. consulate in Peshawar. The Pakistani Taliban claimed responsibility for the operation. Eight people, including three militants, were killed. No one in the mission was hurt.
Pakistan has witnessed a jump in violence since bin Laden's death, including a twin suicide bombing last week that killed more than 80 people, most of them paramilitary recruits.
The Taliban have kept up pressure on the government with suicide attacks despite several army offensives against them.
The United States wants nuclear-armed Pakistan to be a more reliable partner in its war on militancy. Cooperation between the two allies is needed to stabilize neighboring Afghanistan.
Ties have been severely damaged since the secret raid that killed bin Laden. Pakistan is under pressure to explain how he spent what appeared to be about five years in a military town not far from the capital.
Pakistan's army was infuriated by the operation, describing it as a violation of the South Asian country's sovereignty.