Officials and witnesses said the explosions, less than 15 minutes apart on Wednesday, took place about 100m from the residence of the US consul and about 200m from the US consulate.
The latter was the scene of a bloody car bomb attack in 2002 blamed on Islamists.
Information Minister Shaikh Rashid said it was too early to say who was responsible for the bombings, but it looked as if they could be connected to al-Qaida.
However, a US State Department official said the target of two car bombs was a privately run English language school and not the nearby residence of the US consul general.
'War on terror'
The official said the car bombs were aimed at the Pakistan-American Cultural Centre which is not affiliated with the US government.
"We have no connection with this facility," the official said. "There are no Americans on its staff and there were no Americans injured."
The use of car bombs has been
common in recent attacks
The policeman died shortly after the blasts in Karachi's Jinnah Hospital, an official there said. The head of the hospital's emergency department, doctor Seemi Jamali, said it was treating 26 wounded.
She said six were seriously hurt including several policemen and Pakistani journalists.
Karachi, Pakistan's biggest city, has been the scene of frequent acts of violence since President Pervez Musharraf joined the US-led "war on terror" in 2001.
The blasts came two days after police in Karachi arrested six members of Harkat-ul Mujahideen al-Alami, an alleged al-Qaida linked group that tried to assassinate Musharraf in 2002.
Karachi police chief Tariq Jamil said the blasts did not appear to have been caused by "suicide bombers", unlike a sectarian attack earlier this month that killed 15 minority Shia Muslims and wounded 125 at a Karachi mosque.
Musharraf has angered many by
backing the United States
Musharraf has stepped up a battle against Islamist opposition since joining the "war on terror" after the September 11 attacks on the United States in 2001.
Islamists enraged by the crackdown and Musharraf's backing of the US-led war in neighbouring Afghanistan have responded with repeated attacks aimed at undermining his government.