The hit-and-run incident occurred shortly before midnight on Interstate 5 and the two victims, both in their 20s, were rushed to Harborview Medical Center, Washington State Patrol Trooper Rick Johnson said on Twitter.
Video of the crash on social media showed a white car striking the women, who flew into the air before landing on the ground.
The Seattle Fire Department said one of the victims was in critical condition while the other is stable with serious injuries.
State troopers and officers from the Bellingham Police Department chased the vehicle as it fled, and nabbed the suspect. Both he and his passenger were uninjured, Trooper H. Axtman said on Twitter.
The unidentified suspect -- a 27-year-old man from Seattle, according to The Associated Press -- was booked in the Whatcom County Jail. Police said he is the same person who attempted to elude officers in another incident two weeks ago.
Protests in Seattle have been ongoing in the wake of George Floyd's death in Minneapolis, which triggered a nationwide movement condemning police brutality and racial inequality.
Authorities have closed I-5 several times amidst the unrest and clashes with police have ramped up after the city cleared the self-declared Capitol Hill Occupied Protest zone on Wednesday following several violent incidents.