Follow the latest news on the US midterm elections 2022
Election results showed Mr Warnock leading Mr Walker by 0.9 per cent, or a little more than 35,000 votes, with 95 per cent of the state's ballots reported.
Libertarian candidate Chase Oliver received 2.07 per cent of the vote.
Georgia law calls for a run-off election between the two candidates with the most votes if no candidate reaches 50 per cent.
The head-to-head election between Mr Warnock and Mr Walker will be scheduled for December 6.
“We saw Georgians from all over this state cast their ballots to make their voice heard. It’s still a wonderful thing,” Mr Raffensperger said.
“This vote, this democracy, this republic — I still stand in awe of what we saw and what our forefathers have built on this nation. Something so unique in human history.”
Mr Warnock, who won his seat in a run-off election two years ago, tweeted a link to a fund-raiser for his run-off campaign after the announcement.
“We're going to a run-off, Georgia! Let's do this one more time!” he tweeted.
“I understand that at this late hour you may be a little tired, but whether it’s later tonight or tomorrow or four weeks from now, we will hear from the people of Georgia,” Mr Warnock told supporters.
Mr Walker did not immediately issue a public comment.
Meanwhile, the incumbent Georgia senator has distanced himself from the president and portrayed himself as a pragmatist.
Mr Warnock has promoted deals he made with Republicans on infrastructure and his sponsorship for putting a cap on drug prices.
The result of the run-off could determine which political party controls Congress, but other seats remain in play.
Democratic incumbents face tough races in the south-western states of Arizona and Nevada.
In Arizona, incumbent Mark Kelly leads Trump-endorsed Republican Blake Masters by five per cent of the vote, with 68 per cent of the state's ballots counted.
And Catherine Cortez Masto, the incumbent senator in Nevada, trails challenger Adam Laxalt by three per cent with 75 per cent of the vote's in.
Either party can win control of Congress if they win both seats.
Two Republicans lead Alaska's US Senate race, meaning that seat will probably go to that party.
AP contributed to this report