The Twitter account that sent the threat @Lucy_Loobie remains active and has tweeted defences of itself.
The account, which says it is shared between several people, said to one person: "It was about time running out not a bomb you silly people."
The Labour Against Antisemitism campaign group, for whom Ms Sharpe is a spokesperson called the tweet a "disgusting" threat.
"Labour Against Antisemitism will not tolerate threats of violence against our activists - this has been reported both to the CST and the police," they said.
