The spokeswoman said the roadblock from which the couple fled was targeting drugs and that police abandoned the foot chase after concerns for their own safety near the water in the dark.
Territory Duty Superintendent James O'Brien said the two are thought to have jumped into the water.
"We believe the pair may have jumped into the Mary River and we hold grave concerns for their welfare," he said.
"The Mary River system is full of salt water crocodiles and we are hoping that these people have made it to safety."
Police did not respond to questions about why they thought the couple may have fled.
Emergency services were sent to the scene of the couple's disappearance early Saturday.
Duty Supt O'Brien said the couple should not be approached.
A police spokeswoman could not confirm if the couple are thought to be dangerous.
Both are described as being of indigenous appearance.
Mr Woodhouse is 175cm tall and of medium build, while Ms Munnich is 160cm tall with long hair.
Sightings of people matching the couple's description should be reported to police on 131 444 or Crime Stoppers on 1800 333 000.