Iraqi police also fired tear gas and stun grenades to scatter hundreds of pro-Iranian protesters gathered outside the Green Zone in the capital Baghdad, where the US Embassy is located.
"Death to Israel, death to America," the protesters shouted.
Pakistan and Iraq have the largest Shi'ite Muslim populations after Iran.
In Karachi, protesters were pushed back from the consulate, a spokesman for the local government said, after they set a vehicle ablaze outside the main gate and clashed with police.
At least nine people were killed, police said, but it was not immediately clear how.
The US Consulate in Karachi and the US Embassy in Islamabad did not respond to requests for comment.
"We're safe," a diplomat in the compound said.
Reuters reporters heard sounds of gunfire and saw tear gas being fired in streets around the compound.
Video footage showed protesters holding pictures of Khamenei and chanting "Death to America" before the clashes erupted.
Large protests also occurred in other parts of Pakistan.
Protesters set fire to a United Nations office building in the northern city of Skardu, in the normally peaceful Shi'ite-majority Gilgit Baltistan region known for its Himalayan peaks popular with tourists.
"A large number of protesters have gathered outside the UN office in GB and burned down the building," local government spokesman Shabbir Mir told Reuters, adding no casualties had been reported.
Earlier in the day, in the central city of Lahore, hundreds of protesters gathered outside the US consulate.
There were some small-scale clashes with police but no reports of violence.
"Some of the protesters tried to damage the security gate, hundreds of yards away from the consulate. However, police stopped them without use of force," Aqeel Raza, an eyewitness, told Reuters.
In the capital Islamabad, all roads leading to the Red Zone, which houses diplomatic missions and parliament, were blocked to traffic, police said.
Western diplomatic missions in Pakistan have stepped up security protocols, according to diplomatic sources, restricting staff movement across the country as tensions flare.
Several multinational companies operating in Pakistan are also reviewing the situation, corporate sources said, discussing measures including limiting air travel and enhancing security around offices and factory sites.
