Judge Jeanine Pirro, a legal pundit for the US news channel, also accused the Somali-American congresswoman of being anti-Israel and a believer in sharia law.
Her bizarre claims came amid the continuing fallout over comments made by Ms Omar last week in which she said she was being pressured to pledge “allegiance” to Israel.
“Think about this, she’s not getting this anti-Israel sentiment doctrine from the Democrat party, so if it’s not rooted in the party, where is she getting it from?” Ms Pirro said on her Justice with Judge Jeanine show on Saturday evening.
“Think about it. Omar wears a hijab, which according to the Quran 33:59 tells women to cover so they won’t get molested. Is her adherence to this Islamic doctrine indicative of her adherence to sharia law? Which in itself is antithetical to the United States constitution?”
Despite Ms Pirro’s claims, there is no evidence Ms Omar has ever proposed sharia law or expressed opposition to the US constitution.
Brian Klaas, an American political scientist at University College London, called Ms Pirro’s comments “blatant and absurd Islamophobia from a close ally of President Trump”.
“Will *any* Republicans condemn it?” he added, after a number of GOP lawmakers urged the Democratic leadership to punish Ms Omar over her Israel comments.
Qasim Rashid, a lawyer and human rights activist, tweeted: “Will anyone on the Right condemn this blatant xenophobia? Per Pirro logic, are Catholic Nuns against US Constitution too [because] of their habits?”
In a statement, Fox News told The Independent: “We strongly condemn Jeanine Pirro’s comments about Rep Ilhan Omar. They do not reflect those of the network and we have addressed the matter with her directly.”
Ms Pirro said: “I’ve seen a lot of comments about my opening statement from Saturday night’s show and I did not call Rep Omar un-American.
"My intention was to ask a question and start a debate, but of course because one is Muslim does not mean you don’t support the Constitution.
"I invite Rep Omar to come on my show any time to discuss all of the important issues facing America today.”
In November, Ms Omar defended her wearing of the hijab in Congress, which lifted a 181-year ban on headwear in its chambers to allow her to do so.
“No one puts a scarf on my head but me,” she tweeted at the time. “It’s my choice – one protected by the first amendment. And this is not the last ban I’m going to work to lift.”
According to the Noble Quran website, which provides an English translation of the religious text, verse 33:59 reads: “O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused.”
On Friday, the House passed a resolution by 407-23 condemning antisemitism and other forms of hate in response to Mr Omar’s comments.
Friday’s measure condemned antisemitism as “hateful expressions of intolerance that are contradictory to the values and aspirations that define the people of the United States”. It also condemned anti-Muslim discrimination and bigotry.
“I want to talk about the political influence in this country that says it is OK for people to push for allegiance to a foreign country,” Ms Omar told an audience in Washington last week.
She later doubled down on her comments, tweeting she should not have to “have allegiance/pledge support to a foreign country” in order to serve in Congress.
Ms Omar’s comments were also criticised by a number of Democrats, with some claiming the suggestion of “allegiance” to Israel invokes antisemitic tropes.
But Ms Omar received support from Alexandria Ocasio-Cortez, who said the criticism of Ms Omar was "hurtful" and that “discussion and debate on this issue is fair and merited”.
Ms Pirro supported Mr Trump in the 2016 presidential election and has become known for delivering passionate defences on Fox News of the president.
She has supported Mr Trump's claims federal investigations into his administrations are a "witch hunt", and last year posed in the White House with Mr Trump and her book Liars, Leakers, and Liberals: The Case Against the Anti-Trump Conspiracy.