Officers found the bodies in a home in a southern neighborhood of the city after being alerted by neighbors, who heard gunshots at around 1930 GMT, state-run Hina news agency reported.
"Six corpses have been found by police in the Kajzerica district of New Zagreb," the agency reported, citing a police source, AFP reported.
A police spokesperson could not immediately be reached for comment.
According to the initial investigation, the victims appeared to have been shot dead by a firearm, Hina reported, without providing details on their ages or identities.
Police have sealed off the city as they search for the suspect, the report added.