The user, who calls herself Amanda Bieber, prompted a viral feud when she suggested that Bieber is "much bigger" than the late Nirvana frontman.
She tweeted: "Justin Bieber is much bigger than Kurt Cobain, so shut up. Did Kurt Cobain ever have the biggest fanbase on Twitter? NO."
The post was retweeted over 5,000 times, with angry fans of Cobain complaining about the teen's "disrespect".
However, the poster has continued to make disparaging remarks about Cobain, as well as other iconic musicians including Michael Jackson and Freddie Mercury.
She added: "Kurt Cobain is trending because of my tweets about how Bieber is much better than him. I made you relevant Kurt, you owe me!"
Bieber has yet to comment on the messages, although the individual has tweeted at him directly, saying: "Justin I love you so much please follow me."
It has been suggested that the user may be a 'troll' deliberately attempting to cause controversy.
Bieber recently revealed that he considered retiring from music after a woman claimed he was the father of her 3-month-old child.