According to the surveys, the centre-left Fernandez, 54, would obtain 42-46 per cent of the vote and would not need a runoff to be declared president-elect.
Preliminary official results were expected later Sunday.
The closest of her 13 rivals, Christian Liberal Elisa Carrio, would only get 23-25 per cent of the ballots, exit polls showed. Some 27 million Argentine citizens were entitled to vote.
To avoid a run-off, the winning candidate must reach one of two results: at least 45 per cent of the vote, or 40 per cent with a lead of more than 10 percentage points above the second-place finisher.
Preliminary official results were expected later Sunday.
Polls opened at 1100 GMT and were originally scheduled to close 2100 GMT. Electoral authorities extended voting in Buenos Aires by one hour after some polling stations were delayed in opening, and because of many long queues.
No serious incidents were reported.
In theory, no exit polls are allowed to be made public before the first official results are known, although Argentine media have a history of violating this embargo.
"Today is a very special day. When I was 18 I could not vote," Fernandez said when she cast her ballot in the southern city of Rio Gallegos.
"Nobody could decide on anything," Fernandez recalled, with reference to the dictatorship of 1966-73.
Outgoing President Kirchner (2003-2007) also stressed the importance of "institutional normality" as he cast his ballot.
Carrio voted in Buenos Aires and claimed she was "very happy and very calm" awaiting the result of her campaign.
The new president is set to be inaugurated on December 10.
