Bradford West MP Naz Shah told the House of Commons she "profoundly" regretted the posts made in 2014, before she became an MP.
Shah shared a graphic of Israel superimposed onto the United States under the words "Solution for Israel-Palestine Conflict -- Relocate Israel into United States", adding the comment: "Problem solved."
She also used the hashtag #IsraelApartheid above a quote saying "Never forget that everything Hitler did in Germany was legal".
Shah and party leader Jeremy Corbyn had "mutually agreed that she is administratively suspended from the Labour Party ," a party spokesman said.
"Pending investigation, she is unable to take part in any party activity."
Corbyn called the comments "offensive and unacceptable", but initially declined to suspend Shah, a decision described as "quite extraordinary" by Prime Minister David Cameron.
Shah quit as a parliamentary assistant to shadow chancellor John McDonnell on Tuesday before making the apology to parliament on Wednesday.
"I accept and understand that the words I used caused upset and hurt to the Jewish community and I deeply regret that," she said.
"Anti-Semitism is racism, full stop."
Corbyn has been urged to distance himself from far-left activists accused of anti-semitism .