One went off in a minibus as 30 students were preparing to board it.
At least 11 people were injured, including a 40-year-old teacher, and the vehicle was completely destroyed.
Each bomb contained 400 grams (14 ounces) of explosive and was fitted with a timing device, bomb disposal experts told the AFP news agency.
There is no indication of who carried out the attack outside the Ashraf-ul-Madaris religious school.
The school has about 2,000 students, including Afghans and children of Pakistanis living in foreign countries. Most live in the school hostel.
Karachi has experienced a wave of ethnic, religious and political violence which has left hundreds of people dead over the past few years.
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