The decision was announced on Israeli television station Channel 12, which cited Israeli Interior minister Arye Deri as having made the decision.
It comes just four days after reports indicated that Donald Trump told advisers he believed Israel should enforce its 2017 law that allows individuals to be denied entry into the country if they have supported boycotting Israel.
The White House has denied Mr Trump expressed such an opinion, with press secretary Stephanie Grisham telling Axios earlier in the week: "The Israeli government can do what they want. It's fake news."
The decision by Mr Deri, whose post grants him the power to approve visas, would likely have been made after consultation with prime minister Benjamin Netanyahu, and comes roughly a week after the United States House of Representatives voted in opposition to the Boycott, Divestment, and Sanctions (BDS) movement, which seeks to force the end of international support of Israel's occupation of Palestinian lands.
The resolution disapproved of BDS tactics, "including efforts to target United States companies that are engaged in commercial activities that are legal under United States law, and all efforts to delegitimize the State of Israel." The measure received overwhelming support in the House, with just 17 voting against it, including Ms Omar and Ms Tlaib.
Even so, the decision by Mr Deri was quickly criticised by foreign dignitaries, including by Dan Shapiro, a former US ambassador to Israel who wrote on Twitter that the decision would hurt Israel's relationship with the US while boosting BDS.
"Original Israeli decision to allow Tlaib/Omar visit was wise. Reversal makes little sense. I disagree with their stands on Israel, have criticised them," Mr Shapiro, who served during the Obama administration, wrote. "But zero harm in letting them come learn, see (even if they had an agenda). Reversal harms Israel's standing in US, boosts BDS."
Requests for comment sent to the offices of Ms Omar and Ms Tlaib were not immediately returned. The White House has not commented publicly on the reported decision.