Miley posted a screen grab of some of Sinead's tweets, which reference a need for urgent psychiatric help.
The 'We Can't Stop' singer said that "before Amanda Bynes" there was Sinead.
Amanda is currently being treated at a private rehabilitation facility for her psychiatric problems, while Sinead has spoken openly about her own battles with depression and suicide attempt, and was also hospitalised last year.
Miley said in a recent interview with Rolling Stone magazine that her 'Wrecking Ball' video - in which she appears naked on a giant demolition ball - was inspired by Sinead’s 90s hit 'Nothing Compares 2U'.
Sinead responded by pening an open letter to the 20-year-old saying that the music industry “doesn’t give a s**t about you” and “will prostitute you for all you are worth”.
If you've been affected by the issues in this article, please call the Samaritans on 08457 90 90 90.