Although formal identification has not taken place, City of London Police said it believed the body found was that of the Year 8 Ark Globe Academy pupil, who went missing more than a week ago.
He was said to have been travelling with a friend on a bus but did not arrive at the school in south London last Tuesday.
The school's executive principal Matt Jones told parents in a letter that the boy was in full school uniform but exited near the bridge, before his usual stop closest to the school in Elephant and Castle.
He then fell into the River Thames, Mr Jones said.
A body was recovered by police marine units on Wednesday.
City of London Police said in a statement: “At around midday on Wednesday 28, a body was recovered from the River Thames by marine units which we believe to be that of a 13-year-old who has been missing since Tuesday 20 April.
“His family have been informed but at this time formal identification has not yet taken place.”
Additional reporting by PA
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