"While we cannot comment on the specifics of an ongoing investigation, I can confirm that the Democratic Party of Georgia is under investigation for possible cyber crimes", Press Secretary of the Georgia Secretary of State Candice Broce said in a statement.
Asked about the investigation on CNN's State of the Union, she said: "I've heard nothing about it".
"I want to make it very clear to all of the press, everybody, I am not here because I am making some grandstand because I am thinking about running myself", she said.
Abrams, a graduate of Yale Law School, was the minority leader in the Georgia State House of Representatives and is in a closely fought race against Georgia GOP Secretary of State Brian Kemp to succeed Republican Gov. Nathan Deal.
In the call, which was obtained by Channel 2 in Atlanta, a man pretends to be the media giant Winfrey, who campaigned alongside Abrams on Thursday. "I don't want to run". If elected, Abrams will be the first African-American female governor in the United States.
"I am an independent woman; I have earned the right to do exactly what I want to do when I want to do it".
Oprah also gave an impassioned speech in Marietta, calling on people to vote and saying, "For anybody here who has an ancestor who didn't have the right to vote, and you are choosing not to vote - wherever you are in this state, in this country-you are dishonoring your family".
Abrams on Sunday said that the difficulties faced by many first time voters has only galvanized more people to head to the polls.
More than 1.5 million Georgians already have cast ballots.
The Road to Power, a white supremacist and anti-Semitic video podcast hosted by Scott Rhodes of Idaho, is the group behind the robocall. "This is the South. People have been really wonderful and really optimistic about Stacey Abrams".
Republican gubernatorial candidate Brian Kemp still leads the Secretary of State's office despite being a candidate for governor.
The headline "AFTER FAILED HACKING ATTEMPT, SOS LAUNCHES INVESTIGATION INTO GEORGIA DEMOCRATIC PARTY" sat front-and-centre on the secretary of state's government website - directly beneath a voter's guide to polling locations.