The police said at least one suspect was being sought in connection with the incident, which took place on Wednesday. Footage from the scene showed officers tending to casualties on the pavement near Third Avenue and Pine Street, BBC reported.
Police chief Carmen Best told reporters at the scene that one woman had been killed and several people were wounded. Officials at Harborview Medical Centre, where all the wounded were taken, said seven people were being treated, including a nine-year-old boy, reported Aljazeera.
Tyler Parsons, who works at a nearby coffee shop, told the the Seattle Times newspaper that he saw victims suddenly falling to the ground. He said several people ran into his shop to take cover.
"The shooting was just kind of terrifying," he told the paper.
It was the third shooting in the area in less than two days and the latest in a string of incidents that have affected schools, churches, cinemas and other public places across the US.
Police have also ordered people to stay out of the area and have shut down a subway station as they searched for one or more suspects.
Approximately 40,000 people have died from various firearms-related incidents, including suicides and murders, in 2017 in the US, according to government figures.
( With inputs from IANS )