Réada Cronin linked Israel to Nazism, questioned the fluoridation of the public water supply, and used offensive language.
She also replied to another Twitter account which suggested "loads of judges are paedophiles" by saying "wouldn't surprise me."
Leo Varadkar has criticised her remarks, saying that Sinn Féin is "not a normal party" and that its mask has slipped again.
The Kildare North TD has apologised, and says she "never intended to cause hurt or distress to anyone."
