In a statement posted on Twitter, McCaskill said her decision is not based on recent allegations that Kavanaugh, now a federal judge, assaulted a girl in high school, which Kavanaugh denies. Monday's rule: Christine Blasey Ford must be heard.
Ms Debra Katz, a lawyer for Ms Ford - who only came forward publicly on Sunday after trying to keep her name hidden for more than a month - had said earlier she was ready to speak under oath before the Senate Judiciary Committee.
The standoff left both parties gambling over which of their approaches would appeal to voters in November's elections, which will determine House and Senate control.
Ford is now a psychology professor at California's Palo Alto University, while Kavanaugh is currently a judge on the U.S. Court of Appeals for the District of Columbia, widely viewed as the nation's second most powerful court.
Republicans have largely stood by Mr Kavanaugh's denials.
Of the Senate women, six are Republicans.
Whether Kavanaugh and Ford testify under oath, and to what details, has enormous stakes for President Donald Trump and the November 6 midterm elections - not to mention American men, women, teenagers, parents, schools and anyone who rises to the top of a profession in the #MeToo era.
"We had a good saying that we've held firm to this day as the dean was reminding me before the talk, which is what happens at Georgetown Prep stays at Georgetown Prep", he told the audience.
That remark was noteworthy because most Republicans have handled the question of Ford's credibility more gingerly.
"She, Dr. Ford, decided, perhaps reluctantly, that she wanted the world to know information about his qualifications for the court", he said.
The vote on Kavanaugh's Supreme Court nomination has been suspended at least until senators have had a chance to hear from the judge and his accuser.
Ms Ford has contended that at a house party in the 1980s, a drunken Mr Kavanaugh tried undressing her and stifling her cries on a bed before she fled. The elite high school also graduated President Donald Trump's other Supreme Court appointee, Neil Gorsuch, and Federal Reserve Chairman Jerome Powell.
If the judiciary committee's timetable slips, it would become increasingly hard for Republicans to schedule a vote before midterm elections on November 6, when congressional control will be at stake.
There were signs the GOP's strategy of planning a nationally televised hearing yet also offering Ford the option to testify privately was keeping possible Republican defections in check. "Senators must decide what standard to apply in deciding whether Judge Kavanaugh should be confirmed, and we need to find actionable facts and evidence", the Utah Republican wrote in an op-ed for the Washington Examiner.
"I, by coincidence, three classmates of mine at Georgetown Prep were graduates of this law school in 1990 and are really, really good friends of mine", Kavanaugh said in a recording of the full speech, naming his friends.
"Look, if she shows up and makes a credible showing, that will be very interesting and we'll have to make a decision".