Morgenstern, who played the figure of Mary in Mel Gibson's The Passion of the Christ and runs the Jewish State Theatre in Bucharest, published an email she received in which the author threatens to violently kill Morgenstern and her children, as well as set fire to the Jewish theater and its staff.
The email was signed "on behalf of the far right Alliance for Uniting Romanians (AUR)," although its leader George Simion condemned the threat, saying it was not issued by the party, and urged authorities to quickly find and punish its author.
Police said they were tracking the IP address of the email sender.
The ultra-nationalist party AUR was formed a year ago and surprised in a December general election to become the fourth-largest party in parliament.
Unlike some of its central and European peers, Romania did not have a mainstream party supporting far-right ideas until December's parliamentary election, although these had surfaced in well-established parties too.
Romania was an ally of Nazi Germany until August 1944, when it changed sides, and hundreds of thousands of Romanian and Ukrainian Jews and Roma were killed in areas it controlled.
The European Union state has only in recent years begun to come to terms with its role in the Holocaust, admitting for the first time in 2003 that it took part. Sensitivity towards the Holocaust and knowledge of it remain patchy.