There has been one recorded case in King County, which is the area around Seattle.
The centre adds that while it is expected that most travellers will be immune to measles, some individuals will be susceptible, including infants less than one-year-old or people who have never been immunized against measles.
Most of the cases involved children younger than 10, the Clark County Public Health Department said in a statement.
Susceptible Clark County and OR locations include schools in Battle Ground and Vancouver, Portland International Airport and a number of churches.
Additionally, Washington's Emergency Operations Center is coordinating resources to support the state Department of Health and local officials to reduce impacts of the outbreak, and assess for any possible long-term effects.
Around 88 per cent of children in the province have been sufficiently vaccinated against the disease.
As of Saturday, there are 32 confirmed cases of measles in Washington - an outbreak that has already prompted Gov. Jay Inslee to declare a state of emergency.
The outbreak appears to have already spread to neighbouring OR, with one related case reported.
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This is the first confirmed case of measles in Oregon.
Health officials have warned that people infected with the disease had visited schools, churches, a dentist´s office, a Costco store, an Ikea store and the Portland airport.
The measles vaccine has been part of routine childhood shots for decades, and measles was declared eliminated in the U.S.in 2000. The measles vaccine is very effective. No cases related to the Clark County outbreak have been reported in the province, but B.C.'s vaccination rate now sits below the 95 per cent necessary to achieve herd immunity.
Measles is highly contagious and can be spread when an infected person coughs or sneezes.
Two doses of the vaccine in childhood are 97 percent effective and provide lifetime immunity.
Measles symptoms begin with a high fever, cough, runny nose and red eyes, followed by a rash that usually begins at the head and spreads to the rest of the body.
Marissa Armstrong with Clark County Public Health said people who have measles symptoms should contact their health care provider ahead of going into a clinic.