The rapper was supposed to be on the cover of the magazine's new issue, but was replaced with the late Philip Seymour Hoffman. Drake tweeted Thursday that he's "done doing interviews with magazines."
"I just want to give my music to the people," he wrote. "That's the only way my message gets across accurately."
Other Thursday tweets from the 27-year-old were deleted, including one about his discomfort with Hoffman gracing the cover of Rolling Stone.
"I'm disgusted with that. RIP to Phillip Seymour Hoffman. All respect due. But the press is evil," he tweeted.
In the interview, Drake talks about growing up as a biracial child in Canada, meeting his mentor Lil Wayne and launching a successful career in pop and rap.
Drake also discussed not attending last month's Grammy Awards, where he lost three rap trophies to Macklemore & Ryan Lewis, including best rap album, which Drake won last year. Macklemore & Lewis also beat Kendrick Lamar, Jay Z and Kanye West in the latter category.
Macklemore sent a text to Lamar—and posted the message online—after the awards show, telling Lamar he felt that he had robbed him by winning best rap album.
"I was like, 'You won. Why are you posting your text messages? Just chill.
Drake also tweeted Thursday that he never spoke of West's "Yeezus" album during the interview. Rolling Stone quotes Drake calling some of West's lyrics "questionable," along with him saying he "loves" the outspoken rapper.
"I never commented on Yeezus for my interview portion of Rolling Stone," he tweeted, which was deleted.
Rolling Stone said in a statement to The Associated Press that "we stand by our reporting."
A representative for Drake didn't immediately return an email seeking comment.
The new issue of Rolling Stone hits newsstands Friday.
Follow Mesfin Fekadu at: twitter.com/MusicMesfin