A senior provincial police officer however said that three people had died in that blast.
"Police had spotted the suicide bomber who began to ran away and before being caught blew himself up, killing three civilians and wounding several people, including police," Wazir Badshah told reporters close to the scene.
Hospital officials later said that seven people were killed in total in both blasts, although some reports said that as many as 17 people were killed altogether.
Taliban blamed
No one claimed responsibility for the bomb, but shopkeepers said the Taliban may have targeted the shop as local people regularly download music into their mobile phones there.
The Taliban have targeted music shops and banned music, film and videos during their 1996-2001 rule of Afghanistan.
General Mohammad Ayub, the provincial police chief, said that the tribal dispute was the cause of the earlier market blast however.
The city of Khost has been the scene of several attacks by the Taliban in recent weeks.