Big Hit Entertainment, the company behind the pop band, says it is taking action over posts "that exceed the reasonable and accepted boundaries of expression and personal commentary".
The firm did not go into detail about the nature of the comments.
However, it has previously sued over claims of "sajaegi" - bulk-buying albums to inflate BTS's chart position.
Earlier this summer, the company also asked for court authorisation to seize and destroy bootleg merchandise being sold outside the band's concerts.
In a statement, Big Hit explained it routinely monitored social media and message boards for posts about its artists that contained "ill-intentioned criticism, the spreading of groundless information and personal attacks".
It has also established a hotline for fans to report offensive or defamatory content.