Johnson says she's now receiving death threats on Twitter from Brown's supporters.
The fight started when 23-year-old Brown posted a picture of himself, saying he looked old. Johnson replied: "I know! Being a worthless piece of (expletive) can really age a person."
Brown fired back a series of crude sexual jokes. Johnson posted a link to a news story about Brown's 2009 assault on singer Rihanna.
Before deleting his account, Brown wrote: "Just ask Rihanna if she mad---" The on-again-off-again couple have been seen together recently.
A representative for Brown's record label didn't immediately respond Monday to an email seeking comment.
Brown had 11.6 million followers on Twitter.