The Aug. 3 edition's cover makes Tsarnaev look more like one of the rock stars who usually grace it than a suspect in a high-profile bombing.
In the photo, the 19-year-old is sporting shaggy hair and staring intently into the camera.
A preview on the magazine's website says the story by contributing editor Janet Reitman traces how "a bright kid with a charming future became a monster."
In the preview, the magazine says Reitman spent two months talking to "childhood and high school friends, teachers, neighbors and law enforcement agents" about Tsarnaev and the investigation into the bombing.
Some people have already taken to Twitter and Facebook, saying the cover is a glamorization of Tsarnaev, calling the decision to use the photo disgraceful.
The cover has garnered more than 6,000 comments on the magazine's Facebook page, mostly denouncing Rolling Stone's decision to feature the suspect.
Boston Mayor Thomas Menino, who sent a letter to the publisher of Rolling Stone, says the cover "rewards a terrorist with celebrity treatment" and that the focus should be on survivors.
"Why would they publicize a guy who destroyed people's lives? It doesn't make any sense to me. Very poor taste," said Menino.
The magazine hits newsstands Aug 1. Two New England-based retailers announced on Wednesday that they will not carry the magazine in their stores: Woonsocket, R.I.-based pharmacy chain CVS, and a Rockland, Mass.-based convenience store chain, Tedeschi Food Shops.
The magazine's editors issued the following statement regarding the issue:
"Our hearts go out to the victims of the Boston Marathon bombing, and our thoughts are always with them and their families. The cover story we are publishing this week falls within the traditions of journalism and Rolling Stone's long-standing commitment to serious and thoughtful coverage of the most important political and cultural issues of our day. The fact that Dzhokhar Tsarnaev is young, and in the same age group as many of our readers, makes it all the more important for us to examine the complexities of this issue and gain a more complete understanding of how a tragedy like this happens."
Tsarnaev pleaded not guilty to 30 counts associated with the bombing. Investigators say he worked with his older brother, Tamerlan Tsarnaev, to set off two bombs near the finish line of the Boston Marathon on April 15, killing three people and injuring more than 260 others.
The Associated Press and ABC News contributed to this report.