Aidan Rooney, 13, got into difficulty in the water near Garrion Bridge in Larkhall at around 3:15pm on Sunday.
The youngster was taken to Glasgow's Royal Hospital for Children by paramedics, but was later pronounced dead.
Speaking at First Minister’s Questions on Thursday, Ms Sturgeon told MSPs: “Can I extend my deepest and sincere condolences to Aidan's family.
“Aidan, of course, the young boy who tragically lost his life in the Clyde last week.
“I cannot even begin to understand the impact on his family on his friends, and on the wider community as well.”
The teenager’s death is the latest in a series of incidents involving young Scots getting into difficulty in water.
In April, a 15-year-old girl died while canoeing on the River Tweed, south of Rutherford.
And in June last year, a 10-year-old boy drowned while swimming in Loch Lubnaig, near Callander.
Clare Adamson MSP asked the First Minister what the Scottish Government was doing to prevent tragedies similar to Aidan’s.
The member for Motherwell and Wishaw asked: “As we approach the school holidays, can ask the First Minister what the Scottish Government is doing to promote accident prevention messaging - particularly water safety - to young people and families?”
Ms Sturgeon replied: “Incidents such as these are thankfully rare. Each and every drowning is one to many, and they demonstrate the vital role of initiatives such as drowning prevention week, due to run from this Saturday.
“I support the work of the Royal Life Saving Society and Water Safety Scotland who are working hard to prevent such tragic incidents.
“We will do everything we can to support the work they do, and I encourage people to use the water safety resources that are freely available to ensure that everyone can enjoy water safely over the summer months.
She added: “But for now, I’m sure the thoughts of all of us are with Aidan’s family.”
Relatives of Aidan will hold a vigil in his memory at George Park in Wishaw this Saturday.