Officers were called at 6.22am on Saturday 26 May to a report of a concern for the welfare of a 50-year-old woman who was found in the River Anton near Bridge Street.
Officers attended and the woman was taken to the Royal Hampshire County Hospital in Winchester, where she was pronounced dead.
The woman’s next-of-kin have been informed and are being supported by specialist officers.
The death is being treated as suspicious.
Detective Chief Inspector Ellie Hurd said: “We are continuing to make enquiries into the exact circumstances of what took place.
“A small area near Bridge Street remains cordoned off and it is likely that residents of Andover will see a lot of police activity throughout this weekend and Bank Holiday Monday.
“We would like to hear from anyone who knows what happened or who has any other information that they think could help us.”
A 39-year-old man from Andover has been arrested on suspicion of murder and is currently in police custody.
If you have any information relating to this case, please call 101 quoting reference 'Operation Source', or contact Crimestoppers anonymously.