"Thirteen dead bodies and 39 wounded people were brought to hospital," Aminullah Khan, a doctor at the government hospital in Khost city, the capital of the province which borders Pakistan, told AFP.
A senior local police official requesting anonymity said 20 people were killed and 40 others were wounded.
Humayoun Humayoun, a well-known MP from Khost province, was wounded in the explosion, he added.
No group has so far claimed responsibility for the attack, but suicide blasts have been a weapon of choice for the Taliban in their 13-year battle against the US-backed government and foreign forces.
The bombs often target Afghan security forces, but they have also taken a heavy toll on civilians.
The number of civilians killed and wounded in Afghanistan jumped 22 per cent in 2014, a recent UN report said, as NATO troops withdrew from combat.
The United Nations Assistance Mission in Afghanistan attributed the rise to an intensification in ground fighting, resulting in a total of 10,548 civilian casualties last year.
The Taliban, waging a deadly insurgency since they were ousted from power in late 2001, warned that the announcement would damage any prospects of peace talks as they vowed to continue fighting.
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