With more than 97% of polling places counted, Daniel Scioli of Fernandez's Front for Victory coalition had won 36.86% of votes, while Mauricio Macri of the Let's Change coalition had 34.33%, according to official results
In third place at 21.34% was Sergio Massa, who earlier Sunday said his coalition, United for a New Alternative, did not get the numbers it was hoping for and was not in the top two.
According to the constitution, to win the presidency a candidate must either win 45% of the vote or have an advantage of 10 percentage points over their closest rival.
That means Macri and Scioli are headed for a runoff on November 22.
Fernandez was elected in 2007, succeeding her husband, Nestor Kirchner, who served one term. He died of a heart attack five years ago this week.
She won re-election in 2011.
Both Massa and Scioli, whom Fernandez endorsed as her successor, anticipated being in a second round of voting.
"It is an irreversible trend at a national level: There is a second round in Argentina," Sen. Ernesto Sanz said from the headquarters of Let's Change before the results began coming in.
Asked about the possibility of a runoff, Alberto Samid, vice president of the Central Market and a close confidante of Scioli, told CNN: "If there is a second round, we will win twice."
A major issue in the election is whether the new leader will end the country's fight against New York hedge funds
, an unresolved debt debacle that has shut out Argentina from much of the global economy while suffering from massive inflation, declining cash reserves and major economic growth.