The quake of magnitude 5.3 struck near the eastern city of Jalalabad in the early hours, the United States Geological Survey (USGS) said, Reuters reported.
"Sunday night's earthquake has caused financial and human losses in Kunar province," Mawlavi Najibullah Hanif, the spokesman for the provincial governor, told the Bakhtar News Agency, adding that casualties could rise.
Initial reports put the toll from the quake at six, with nine injured, said disaster ministry spokesman Mohammad Nassim Haqqani.
Afghanistan is still recovering from a strong earthquake in June that killed more than 1,000 and wiped out villages in its east.