Introductions also ought to feature cautions, according to the European Jewish Congress (EJC) - an umbrella group for several Jewish organisations.
The EJC's recommendations, included in a new "catalogue of policies to combat anti-Semitism" unveiled in Vienna, also cover the Quran.
EJC president, Moshe Kantor said: "Translations of the New Testament, the Koran and other Christian or Muslim literatures need marginal glosses and introductions that emphasis continuity with Jewish heritage [and] warn readers about anti-Semitic passages in them."
Concerns have been raised that certain scriptures have been distorted or misinterpreted in the past to justify persecution against Jews.
The Archbishop of Canterbury Most Rev Justin Welby said in September 2016 that the Church was complicit in the spread of anti-Semitism.
He said: "It is a shameful truth that, through its theological teachings, the Church, which should have offered an antidote, compounded the spread of this virus.
"The fact that anti-Semitism has infected the body of the Church is something of which we as Christians must be deeply repentant. We live with the consequences of our history of denial and complicity."
Other recommendations include every country, organisation and business adopting and implementing a definition of anti-Semitism issued by the International Holocaust Remembrance Alliance.
Dr Christine Joynes, a theology lecturer at Oxford University, told The Times: "The whole Bible needs a health warning to read it through the right critical lens and in historical context."
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.