"One person down. Everyone needs to leave the area immediately," police said on Twitter, adding that the shooting took place as protesters crossed the city's Morrison Bridge.
In a statement, police said the suspected shooter had been in a vehicle on the bridge when there was a confrontation with a protester.
"The suspect got out of the vehicle and fired multiple shots injuring the victim," the statement added.
The victim was treated at the scene before being taken by ambulance to a Portland hospital with non-life-threatening injuries.
Police are still looking for the suspect, described as an African-American male in his late teens.
Protests are taking place in several US cities for a fourth straight night since Donald Trump's shock election victory, including in Miami, Atlanta, Philadelphia, New York, San Francisco and Portland.
In downtown Portland, protesters blocked traffic and threw objects at police dressed in riot gear who responded with pepper spray and flash-bang devices.
At one point, police pushed protesters back and appeared to take at least one person into custody, according to footage on a local NBC affiliate.
The protesters are voicing anger at President-elect Donald Trump's inflammatory and often deeply controversial campaign rhetoric about immigrants, Muslims and women.
Hundreds of protesters marched through the streets of Los Angeles, blocking traffic as they waved signs in opposition of Mr Trump and chanted "We reject the President-elect" and "Whose streets? Our Streets".
Several thousand activists marched through downtown Miami, with a few hundred making their way onto a highway, halting traffic in both directions.
In New York, demonstrators again gathered in Washington Square Park and by Trump Tower, where the Republican President-elect lives, on Fifth Avenue.
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