There was no claim of responsibility for the attack, which coincided with the start of a meeting in Pakistan aimed at getting a stalled peace process with the Taliban back on track, Reuters reported.
Khost, on the border with Pakistan, has been relatively calm in recent months but last year dozens of people were killed in two suicide bomb attacks in April and July.
On Monday, officials from Afghanistan, Pakistan, China and the United States met in Islamabad in a bid to restart a peace process that broke down in July when news was announced that Taliban leader Mullah Mohammad Omar had died two years earlier.
The announcement led the Taliban to pull out of the talks after just one meeting hosted by Islamabad. A subsequent power struggle within the Taliban has raised questions about who would represent the insurgents if and when the talks with Kabul are restarted.