Police Chief Don Brown says a teenage boy and his parents brought the cub to the police station in a large plastic storage bin on Monday.
The boy found the cub whimpering in the bushes outside his house in the town of Myrtle Creek. He said the mother bear was nowhere in sight.
Still, Brown said it was dangerous to pick up the cub, because the mother bear could have spotted him and attacked. Adult female black bears can weigh up to 35kg.
The 5.44kg female cub was "very well behaved", while spending the night at the station, Brown said.
Police and Oregon department of fish and wildlife officials looked for the cub's mother the next day using a device that mimics a cub distress call, but couldn't find her.
Oregon is home to 25,000 to 30,000 black bears. Myrtle Creek, 145km south of Eugene, has an abundance of wildlife, "but nobody has brought in a bear in the last nine years I've been here", the police chief said.