Police spokeswoman Debbie Willis says the driver was robbed late Tuesday morning while leaving a Bank of America branch in Monroe.
The robber grabbed a money bag and ran about 100 yards to a creek that runs into the Skykomish River.
One witness reported the man floated off on an inner tube. Another said he swam to an inflatable raft that may have been made from an inner tube.
By the time police arrived, he had floated away.
Willis says investigators believe the man could have been picked up by accomplices at a nearby boat launch or park.