Officials said there was no evidence that the teenager and the boy knew each other.
Witness Nancy Barnfield, 47, was at the viewing gallery with a friend who heard a "loud bang," Britain's Press Association (PA) reported.
She told PA she then saw a woman screaming: "Where's my son, where's
my son?"
She said the teenaged suspect was being held by others in the platform area and he "just stood there and was quite calm," PA reported.
The 10th-floor viewing platform is a highlight for visitors of the popular museum, housed in a former power station overlooking the Thames river and typically visited by many hundreds of tourists and families at weekends.
Officials at the museum, one of the world's largest museums of contemporary art, said it would remain closed for the rest of the day as police investigated the incident.
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