Khaama Press said the Taliban claimed responsibility for the attack, saying it was in retaliation for this week's execution of Taliban prisoners by the Afghan government.
The report, quoting local officials, said up to 90 people, including women and children, were injured in the attack.
Shahidullah Shahid, a spokesman for the governor of the province, said the target of the attack were the Afghan and coalition security forces, who jointly use the military base near where the explosion occurred.
Referring to the executions, officials told the BBC most of the 14 prisoners executed so far were criminals, while others were insurgents responsible for deadly suicide attacks in Kabul.
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