The Taliban, which claimed responsibility for the blast, have stepped up attacks amid a bitter leadership transition following the announcement of the death of their leader Mullah Omar.
Observers say the upsurge in violence represents a bid by new leader Mullah Akhtar Mansour to distract attention from the crisis as planned peace talks falter.
"The explosion occurred at the first checkpoint of Kabul airport," said deputy Kabul police chief Sayed Gul Agha Rouhani.
Five civilians were killed and 16 wounded including children, said Kabul police spokesman Ebadullah Karimi.
The toll was confirmed by Kabul CID chief Fraidoon Obaidi, who said the explosion was caused by a suicide car bomb.
Read: Taliban bombing kills up to 29 in northern Afghanistan
Smoke billowed from the scene of the explosion, which occurred during the busy lunchtime period.
An AFP photographer saw pieces of charred flesh strewn around the checkpoint, where passengers undergo the first round of body checks before entering the airport.
Ambulances with wailing sirens rushed to the area and were seen removing bodies from the area, which was strewn with the twisted and mangled remains of vehicles.
Taliban spokesman Zabiullah Mujahid said two vehicles belonging to foreign coalition forces were the target of the attack.
The attack follows a barrage of deadly bombings in the Afghan capital on Friday, which struck close to an army complex, a police academy and a US special forces base and killed at least 51 people.
They were the first major attacks since Mullah Akhtar Mansour was named as the new Taliban chief in an acrimonious power transition after the insurgents confirmed the death of longtime leader Mullah Omar.
Read: Afghan envoy requests Samiul Haq to support peace process with Taliban
Some top leaders of the insurgency, including Omar's son and brother, have refused to pledge allegiance to Mansour, saying the process to select him was rushed and even biased.
Tayeb Agha, the head of the Qatar political office set up in 2013 to facilitate talks with Kabul, resigned last week in protest at Mansour's appointment and two more members of the office followed suit.
The wave of violence underscores Afghanistan's volatile security situation amid a flailing peace process.
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