In a Facebook post in 2014, Ms Shah shared a graphic which showed an image of Israel's outline superimposed onto a map of the US under the headline "Solution for Israel-Palestine Conflict - Relocate Israel into United States", with the comment "problem solved".
Ms Shah's post suggested the US has "plenty of land" to accommodate Israel as a 51st state, allowing Palestinians to "get their life and their land back".
It added that Israeli people would be welcome and safe in the US while the "transportation cost" would be less than three years' worth of Washington's support for Israeli defence spending.
Ms Shah added a note suggesting the plan might "save them some pocket money".
The Guido Fawkes website - which published the post - also pointed to another made before Ms Shah was an MP which used the hashtag #IsraelApartheid above a quote saying "Never forget that everything Hitler did in Germany was legal".
Mr Corbyn - who is under pressure to deal with complaints of increasing anti-Semitism in the Labour Party - said: "What Naz Shah did was offensive and unacceptable. I have spoken to her and made this clear.