The bill now is on its way to Gov. Mary Fallin, a Republican, for final approval.
The governor has not decided whether she will sign the bill, according to her spokesperson Michael McNutt, adding that she needs time to review the legislation.
Once Fallin has the bill she has five business days to decide if she will approve the legislation. If she doesn't sign or veto the bill, it automatically becomes law, according to McNutt.
The Center of Reproductive Rights, has already called on Fallin to veto the bill, which the group says is in "contravention of long standing federal and state constitutional principles as well as basic human rights."
"This bill is as direct an assault on Roe v. Wade
-- and the Supreme Court's subsequent jurisprudence -- as anything we've seen before. If this law is upheld, then (the Roe decision) is meaningless," said Steve Vladeck, a CNN contributor and law professor at the American University Washington College of Law, referring to the Supreme Court decision legalizing abortion.
For purposes of a pregnant woman's constitutional right to choose, the Supreme Court has divided pregnancy into two periods: prior to viability (the point at which a fetus is capable of surviving outside the womb) and from viability to birth, Vladeck said.
"In the latter period, states are allowed to prohibit abortions except where necessary to protect the health of the pregnant woman. But in the former period, states may not place restrictions on abortions that place an 'undue burden' on a woman's right to choose," he said. "Thus, the central problem with the Oklahoma law is its effect on pre-viability abortions. It should stand to reason that a categorical ban on pre-viability abortions (even with an exception where necessary to save the life of the pregnant woman) is, indeed, an 'undue burden,' and is therefore unconstitutional."
The development in Oklahoma comes at a time when the Supreme Court is considering a completely different abortion law from Texas that is more reflective of a new kind of challenge popping up across the country to abortion access. Laws, like the one in Texas, seek to place restrictions on access to clinics.
The Texas law requires doctors to have local admitting privileges and mandates that clinics update their facilities to hospital like standards.
Texas passed the law arguing it was meant to protect women's health, abortion clinics in the states say it is a "sham" law with no medical justification, and its real goal is to block abortion.
Abortion and the 2016 Candidates
Former Secretary of State Hillary Clinton took to Twitter Thursday to condemn the legislature's decision.
"We can't sit by while extreme politicians attack women's basic rights. Not only is this unconstitutional—it's wrong," she tweeted.
Presumptive Republican presidential nominee Donald Trump previously showed interest in the idea of Fallin as a vice presidential candidate.
South Carolina Lt. Gov. Andre Bauer, a Trump supporter, previously said Fallin would be a great choice.
"I think he's going to say, 'Who can help me get the job done?' and I think he needs some balance, and I like Mary Fallin for that reason," Bauer said on CNN's "State of the Union."
Trump tweeted afterward ".@AndreBauer Great job and advice on @CNN @jaketapper Thank you!"
If Fallin approves the bill, critics would interpret the move as being consistent with one of Trump's more incendiary comments on abortion in the past.
On March, MSNBC host Chris Matthews pressured the business mogul to give a yes or no answer to the question, "should abortion be punished."
"There has to be some form of punishment," Trump said during a televised town hall event.
"For the woman?" Matthews asked, to which Trump replied, "Yes."
Trump declined to specify how women should be punished if they underwent an illegal abortion before later issuing a statement backing away from his previous comments.
"If Congress were to pass legislation making abortion illegal and the federal courts upheld this legislation, or any state were permitted to ban abortion under state and federal law, the doctor or any other person performing this illegal act upon a woman would be held legally responsible, not the woman," Trump said at the time. "The woman is a victim in this case as is the life in her womb. My position has not changed -- like Ronald Reagan, I am pro-life with exceptions."
Some members of Oklahoma's Congressional delegation, which is all Republican, told CNN they are watching the bill closely.
Rep. Markwayne Mullin "is a fierce defender of life and supports any policy that would protect the most vulnerable -- babies who cannot defend themselves," said Communications Director Liz Payne.
And Rep. Steve Russell "is watching this issue with interest, and is awaiting the Governor's decision," Communications Director Daniel Susskind said.