Frontrunner Milei was leading in the polls prior to the vote, but Massa — the incumbent Economy Minister — has received 36.2 per cent of ballots so far.
Milei has received 30.2 per cent of the votes, according to the preliminary results.
Meanwhile, Massa and Milei’s rival former Security Minister Patricia Bullrich, who had pledged to restore “order” to the country, garnered 23.8 per cent of the votes.
Sunday’s election saw a voter turnout of 74 per cent, the BBC quoted local media as saying.
After casting his vote in Buenos Aires on Sunday, outgoing president Alberto Fernandez said in a post on X: “I call on every Argentine to defend it and decide the future of the country at the polls.”
Polls before Sunday’s vote had suggested the presidential race could indeed to go to a run-off, the BBC reported.
For a candidate to win outright in the first round they would have needed to secure more than 45 per cent of votes – or 40 per cent plus a margin of 10 percentage points over the closest rival.
As well as choosing its new president and vice-president, Argentinians also voted for 130 new representatives for the lower house of Congress, which has 257 members, and 24 new senators for the 72-member upper house.
The next president will take office in December to start a four-year term.