On Monday, emergency services were called at 3.30pm after reports of an incident on the river.
The body of a 15-year-old girl was recovered from the water a short time later.
Police Scotland Detective Inspector Alistair Sellar said: “We were called around 3.30pm on Monday to a report of a canoeist getting into difficulty on the River Tweed, south of Rutherford, near Kelso.
“Emergency services attended and a rescue operation was launched.
“The body of a 15-year-old girl was recovered from the water a short time later. Her family are aware.
“Inquiries are ongoing to establish the full circumstances of the incident.
“A report will be sent to the Procurator Fiscal.”
The identity of the teenager has not yet been made public by the police.
Kelso provost Dean Weatherston issued a statement, saying: “Myself and the community are deeply saddened by the tragic events of yesterday and our thoughts are with the family.
"She was a lovely young lady with a thoughtful and caring outlook on life and had achieved so much in her young life.
“Her family are a well respected local family who do so much for the community and we’re all sharing their pain today.”