Arsenal, which hosted Sunday's match at Emirates Stadium in north London, said the teenager was sitting with Brazil fans when he threw the banana toward Neymar as he celebrated his second goal in Brazil's 2-0 win.
The club did not give the culprit's identity and Arsenal said there was no sinister motive behind the incident.
"The Metropolitan Police is satisfied there was no racist intent and have confirmed that no further action will be taken," Arsenal said in a statement.
The banana - a fruit sometimes hurled by racist fans at black players - was thrown from the North Stand and landed next to a huddle of Brazil players as they celebrated Neymar's 77th-minute penalty with the 19-year-old striker.
The incident had prompted Neymar to suggest jeers he received from Scottish fans had been racially motivated.
Scotland fans and the Scottish Football Association always denied accusations of racism, and were backed by the officer in charge of policing the match.
The 11,500 members of the Scotland Supporters Club attending the match were located in the South Stand, and the SFA said it wrote to the Brazilian football federation to express their unhappiness at the accusation of racism on the part of their fans.
Supporters did jeer Neymar for much of the match, but only after they thought he had feigned injury following an apparently innocuous first-half clash with Scotland midfielder Scott Brown.
Neymar's on-field treatment held up play and he was then slow in making his way to the sidelines as the referee tried to restart play.
