The musician was buried in "an unadorned pine box" on Thursday, his son Adam wrote in a recent Facebook post.
"My sister and I just buried my father in Montreal. With only immediate family and a few lifelong friends present, he was lowered into the ground in an unadorned pine box, next to his mother and father. Exactly as he'd asked.
"...There's so much I wish I could thank him for, just one last time. Id thank him for the comfort he always provided, for the wisdom he dispensed, for the marathon conversations, for his dazzling wit and humor...And I'd thank him for music; first for his music which seduced me as a boy, then for his encouragement of my own music, and finally for the privilege of being able to make music with him," Adam wrote.
[Read: Leonard Cohen dies at 82 ]
Cohen died last week in Los Angeles. His gravestone is reportedly unmarked, according to The Hollywood Reporter.
"Leonard's wish was to be laid to rest in a traditional Jewish rite beside his parents, grandparents and great-grandparents," read a statement from Rabbi Adam Scheier and Cantor Gideon Zelermyer.