The post suggested the financial cost of deporting Israelis would be “less than 3 years of defense spending” - the "$3bn dollars" the US "spends per year on Israeli defense".
Ms Shah added that the plan would “save them some pocket money“.
The MP confirmed to Guido Fawkes on Monday night that she was responsible for the posts, said she was sorry and would be making a full apology in a statement.
Ms Shah claimed her views on Israel have moderated over the last two years.
In a statement issued by Labour, she said: "This post from two years ago was made before I was an MP, does not reflect my views and I apologise for any offence it has caused."
The JC can reveal that in August 2014, Ms Shah also posted a tweet with a link to a blog which claimed Zionism had been used to "groom" Jews to "exert political influence at the highest levels of public office".
She posted the article, titled "Colonisation, Israel, Palestinian resistance and...", from a blog called Walk Together, which encourages users to "listen and share feelings, ideas and views about Bradford and the world".
But the piece Ms Shah promoted claimed Zionism, "like Al Qaeda, was and is a political movement layered with religious symbolism".
It continued: "Zionism used this and the colonial period to groom other modernised men and women of Jewish descent to exert political influence at the highest levels of public office by using the guilt of the pogroms and offered a solution to the 'Jewish Question' in Europe."
The article concludes: "The reality is that through its historical and current colonial project the Zionist apparatus in Tel Aviv and globally continues to enact policies and practices that are deeply inhumane, that are unequal and have created physical realities that have left the mantra of Tony Blair precisely what it was meant to be an '(un)viable two state solution'."
In July 2014, at the height of the Gaza conflict, Ms Shah posted a link on Facebook to a newspaper poll asking whether Israel had committed war crimes.
She wrote: "The Jews are rallying to the poll." And then called on people to vote "yes".
In January, the Israeli embassy in London complained to Ms Shah after she claimed that no Israeli children had been killed by stone-throwing Palestinians.
During a parliamentary debate on child detainees and prisoners in the Palestinian territories, she said the Israeli government had provided no evidence of Israeli children being killed or injured by Palestinian minors protesting in the West Bank.
When her Labour colleague Ian Austin pointed out that four-year-old Adele Biton had died after being seriously injured when she was hit by a stone thrown by a Palestinian youth, Ms Shah responded that there was no evidence.
Earlier this month Ms Shah wrote to David Cameron to complain that a senior Conservative Party member had made antisemitic remarks at the launch of a local election campaign. An investigation is taking place.
Ms Shah is a member of the Home Affairs Select Committee, which earlier this month announced it would investigate rising Jew-hate in Britain .
A series of Labour members and activists have been suspended by the party in the past two months following allegations of antisemitism.
Conservatives including Finchley and Golders Green MP Mike Freer and Conservative Friends of Israel chairman Sir Eric Pickles have called for the Labour whip to be withdrawn from Ms Shah and for her to stand down from the Select Committee inquiry role.
Mr Freer told Guido Fawkes that Ms Shah was "another example of the poison coursing through Labour".
Joan Ryan, Labour Friends of Israel chair, said: "Both the substance of Naz Shah’s comments, and language used by her, are highly offensive and completely unacceptable.
"As such, they are incompatible with her post as PPS to the Shadow Chancellor. I would also urge our leadership to make clear her views do not in any way reflect those of the Labour Party.
"This incident underlines yet again the need for the Labour Party to take urgent action to combat antisemitism and anti-Zionism in all its forms."
