The bullet came through the wall and struck the woman about 4 a.m. PDT as she slept with her husband and their 1-year-old daughter, the Anchorage Daily News reported.
Police said they received a report of shots fired following a dispute between three young men. Officers who responded to the scene found nearly a dozen shell casings on the street but had made no arrests, the newspaper said.
The victim was treated at a hospital and released within a few hours, her husband said.
The 37-year-old husband, who asked the couple's names be withheld for fear of retaliation, said his wife was on the side of the bed closest to the street and their daughter was between them when the bullet came through the wall.
"When I turned on the light, she was bloody everywhere," he said. "But we didn't know it was a shot -- I thought she cut herself. When I started looking to see, where was the cut, I saw this little hole in her knee. And the bullet was on top of my bed."
He said he left their daughter with his brother-in-law, who also lives in the apartment, and started driving his wife to the hospital, but was stopped by police a few blocks away and she was transferred to an ambulance.