KCPQ-TV said the ship is anchored in Bellingham Bay, north of Seattle.
A police spokesman said officers talked to the ship, the port and the woman and won't be trying to remove her. The ship won't leave for several days.
Earlier, an official with Washington state's Department of Natural Resources said activists protesting Shell's plans for exploratory drilling in the Arctic did some damage to a Seattle dive park.
KIRO Radio reports that DNR spokesman Joe Smillie said divers found cement blocks, cables and chains that were used to anchor a protest barge while kayakers protested last weekend near a Shell oil rig docked in Seattle's Elliott Bay.