She joins Sen. Susan Collins as the second Republican senator to voice her opposition to filling the vacancy before the November election.
"For weeks, I have stated that I would not support taking up a potential Supreme Court vacancy this close to the election," Murkowski said. "Sadly, what was then a hypothetical is now our reality, but my position has not changed."
Collins and Murkowski have each said that the Republican-controlled Senate's move to block the 2016 nomination of Judge Merrick Garland to serve on the Supreme Court guided their decision.
At the time, Senate Republicans argued that the Obama-nominee was being considered too close to Election Day, which was nearly nine months away at the time.
"We are now even closer to the 2020 election -- less than two months out -- and I believe the same standard must apply," Murkowski said in the statement.
Collins, who is currently in a fierce re-election battle in Maine, also said she believes it is too near Election Day to vote on a nominee.
"The decision on a lifetime appointment to the Supreme Court should be made by the President who is elected on November 3rd," Collins said in a statement.
In order to block a Trump nominee, two other Republican senators will need to join Murkowski, Collins and Senate Democrats.
Some Republicans have not yet stated their position, seemingly following the guidance of Majority Leader Mitch McConnell who, in a letter obtained by the Washington Post and confirmed by ABC News, urged his colleagues to "keep your powder dry."
A close eye will be on the Republicans who could tip the balance of a vote, including, Utah Sen. Mitt Romney, the lone Republican to vote in favor of Trump's impeachment at the beginning of the year, and those up for reelection who are especially vulnerable, like Colorado Sen. Cory Gardner.
But some Republicans who were once fiercely opposed to installing Garland on the Supreme Court have now said they will work to push a Trump nominee to the bench.
Republicans, like Senate Judiciary Chairman Lindsey Graham, argue that the situation is different now, with Republicans controlling both the Senate and the White House, compared to 2016 when control was split between the branches.
"I will support President @realDonaldTrump in any effort to move forward regarding the recent vacancy created by the passing of Justice Ginsburg," Graham tweeted Saturday.
In 2016, Graham argued that he believed the vacancy came too close to a presidential election at a time when the Senate and the White House were controlled by different parties.
"If there is a Republican president in 2016 and a vacancy occurs in the last year of the first term, you can say 'Lindsey Graham said let us let the next president, whoever it might be, make that nomination' and you could use my words against me, and you would be absolutely right," Graham said at the time.
McConnell said Friday that a nominee put forward by Trump will receive a vote on the floor of the U.S. Senate, though he's yet to specify a timeline. It's not clear if McConnell intends to lead the Senate in a vote before Election Day.
The timing of the vote could impact how Republicans like Murkowski ultimately side. Her statement Sunday leaves uncertain how the senator might vote during the lame-duck session, especially following an election which has the potential to alter control of both the White House and the Senate.