Tabloid newspaper Bild reported on Friday that Mr Scholz’s bodyguards only realised their mistake later, and chased the man down.
Mr Scholz’s office confirmed the incident, which happened late on Wednesday as the German leader made his way back to Berlin following a celebration for the 25th anniversary of the European Central Bank.
Nobody was hurt in the incident but an investigation into the security breach has been launched.
In a statement, federal police said the man was detained but they declined to provide further details “for tactical reasons”.
Mr Scholz’s spokesperson Wolfang Buechner told reporters in Berlin: “The encounter and hug at Frankfurt Airport (…) was indeed not planned by the Chancellor.
“As such it was a surprise to him, but it wasn’t a big deal in this particular situation,” he added.
“The Chancellor didn’t feel threatened at any point.”
Mr Buechner said Mr Scholz continues to have “full confidence in the work of the police. Nevertheless there are questions surrounding this incident and they will be carefully investigated”.