Lakewood Police Lt. Chris Lawler said authorities found the child after a woman walking home around 1:30 a.m. Monday thought she heard a distressed animal.
Instead, she found an infant boy lying in the grass of a Lakewood residence, Lawler said.
Investigators said the baby was cold but, otherwise, in good health.
He was taken to a local hospital and placed in protective state custody.
Lawler said a female patient at St. Clare Hospital later told officials there she was the child's mother.
"The mother told detectives that she was at a Lakewood residence last night and did some drugs, which made her paranoid," said a Lakewood police news release. "She said she grabbed her baby and ran from the residence because she thought she was being chased. She admitted to leaving the baby in a front yard and hoping someone would find him. She was later found running around the area of 74th and Tyler at 7:07 a.m. and transported to St. Clare for medical treatment."
While detectives were interviewing the mom, the father of the child showed up at the hospital.
He said he last saw his child with his wife Sunday night when he left because he was arguing with her.
He said he didn't know the child had been abandoned.
The child's mother was booked into Pierce County jail for second-degree abandonment of a dependent person.
The father was booked into jail for an outstanding misdemeanor arrest warrant, police said.
Officials haven't identified either of the parents pending official charges.