Another 11 people were injured in the blasts, said Saleem Rasooli, head of Kabul hospitals.
Taliban spokesman Zabiullah Mujahed tweeted that the group carried out the attack, CNN reported.
In recent months, a rash of kidnappings and Taliban bombings have heightened security fears in Kabul, the Afghan capital.
American and other diplomats were barred from traveling the short distance from the city's international airport to their diplomatic missions by road. Instead, they've been ferried by helicopter.
Many countries, including the United States and UK, have had longstanding travel advisories against all but essential travel to Afghanistan because of the security situation.