Ridvan Zykaj, 24, shot dead "eight persons from two Zykaj families in Resulaj village," 90 kilometres (55 miles) south of the capital Tirana, the police said in a statement.
"After the murder the armed person has left the area," police said, adding that the motive was "still unclear".
Police published a photo of the man and asked the public to come forward with any information, warning however that the fugitive "is dangerous" and "should be avoided if seen".
The victims include Zykaj's great-uncle, as well as the great uncle's sons and extended family, police said, adding that the suspect's parents were being questioned.
Local media reported that large police forces have been searching the area.
According to the News24 private television channel, among those killed were a nine-year-old child, a teenage girl and three women.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)