Asked by Swedish public broadcaster SVT if Dylan had received his Nobel diploma and medal Saturday afternoon, Academy member Horace Engdahl said:
"Yes", without making any further comments.
The first songwriter to receive the prestigious award, Dylan has joined a celebrated group of laureates including Thomas Mann, Samuel Beckett, Gabriel Garcia Marquez and Doris Lessing.
The meeting took place at a secret location. The Swedish Academy declined to comment.
The media report came after the enigmatic star performed the first of his two concerts at Stockholm's Waterfront venue, the first stop on a long-planned European tour for his latest album of cover songs, "Triplicate".
His second concert is due Sunday.
Dylan, 75, had not been expected to give his traditional Nobel lecture during the meeting.
The lecture is the only requirement to receive the eight million kronor (837,000 euros, $891,000) that comes with the prize.
He has until June 10 to deliver his lecture, which could be anything from a short speech to a performance, a video broadcast or even a song. Failing that, he risks losing the prize money.