The newborn was discovered Friday evening by a woman who was walking her dog, KOMO-TV, Seattle, reported.
Jeff Myers of the Hoquiam police said officers received a tip that led them to a 21-year-old woman, whose name was not reported, believed to be the birth mother of the baby.
The woman and her boyfriend are being questioned by police, Myers said.
Meanwhile, the woman who discovered the infant told KOMO-TV that the incident was one of the most traumatic experiences of her life.
"I just happened to look up, and there's a wash cloth hanging on a branch," said Diane Smith. The cloth was covered in blood, she said.
"I knew something was wrong, and I went and looked in the woods, and I happened to see this baby laying there," Smith said. "It looked pretty young -- like brand new, almost. I saw part of the face and the ear and a little bit of the arm and hand so ..."
Investigators said they believe the baby was born at the Oasis Motel in Ocean Shore, then left where Smith found it.
Police should have the results of an autopsy on Monday, officials said. At that point they will decide whether to charge the parents.