The vehicle was passing through the crowded M A Jinnah Road in the central part of the city when the explosion occurred, witnesses reported.
“Twelve people were injured, three of them are in serious condition,” Karachi police chief Tariq Jamil said.
The van was carrying as many as 30 passengers and the maimed were admitted to nearby hospitals. Jamil did not say who he thought might be behind the latest explosion, but said the incident appeared to be an act of "terrorism".
The bomb blast comes amid a crackdown by Pakistani authorities on Malaysian and Indonesian students studying at five Islamic religious schools in Karachi.
“Twelve people were injured, three of them are in serious condition”
Karachi police chief
Three people belonging to the Lashkar-e-Jhangvi group were also detained on Thursday.
Among those arrested was the brother of Southeast Asian group Jamaah Islamiyah's alleged operations chief Hambali, who was taken into US custody in August.
A number of explosions have rocked Karachi since Pakistan aided the US in its war against the Taliban in Afghanistan.
It's just not cricket
On 19 September an explosion in a commercial building prompted South Africa to cancel its national cricket team’s tour of Pakistan.
However, the tour was revived after Pakistan excluded restive Karachi and the northwestern city of Peshawar, bordering Afghanistan, from the itinerary.
No one was killed or injured in the building explosion.
Two car-bomb attacks, outside the Sheraton Hotel in May 2002 and the nearby US consulate a month later, killed 26 people including 11 French engineers.