Earlier voting, which is compulsory in Argentina, was extended by an hour after reports of missing ballots and missing poll workers delayed the start of voting.
There have also been allegations of widespread fraud and other irregularities.
Al Jazeera's correspondent in Buenos Aires, Lucia Newman, described the situation as unusually "chaotic".
The exit poll results sparked celebrations at Fernandez's campaign headquarters, but none of the other candidates has so far conceded defeat.
A spokesman Roberto Lavagna, a former economy minister, said he would file a judicial complaint about a "systematic lack of ballots" marked with his name.
Another candidate, Vilma Ripoll, denounced "ballot stealing".
For an outright victory, a candidate needs 45 per cent of the ballots, or at least 40 per cent with a 10-point lead, otherwise a run-off vote will be held on November 25.
|Fernandez supporters began celebrating on the |
streets as poll results were released [Reuters]
According to exit poll results on the TN and Cronica networks, the runner-up, on a distant 24 percent, was a former lawmaker and beauty queen, Elisa Carrio.
The other 12 candidates trailed even further behind.
Fernandez, 54, is a senator with two decades of experience in politics.
If her victory is confirmed, she will take over from her husband in December.
Argentina had its only other woman president in the mid-1970s when Isabel Peron took power after the death of her husband, Juan Peron, but she was not elected to the job.
Kirchner, who is stepping down from the presidency amid high popularity ratings after just one term, has not given any reason for his decision not to run again.
Many Argentines credit Kirchner with pulling the country out of a dramatic economic crisis in 2001 and using growth of 8 per cent a year to create jobs, raise salaries and expand pension benefits
Fernandez herself refused to make any last-minute comments to the media.
Throughout her campaign she gave hardly any interviews and she has remained vague on her policies.
In her final speech on Thursday, she constantly referred to her husband's term and vowed to pursue his left-leaning policies.
She said: "Now we need to work on the remaining dreams."
Fernandez has brushed aside figures suggesting Argentina's economy is overheating with an estimated 20 per cent inflation and low foreign investment.
Instead she has pledged to maintain hefty public spending and price controls, in the hope that the high worldwide demand for commodities that has benefited Argentina will continue.
The first lady has rebuffed critics who have accused her of being excessive in her designer clothes and use of heavy makeup, which have led some to compare her to Argentina's iconic Eva Peron.
"Should I disguise myself as a poor person to be a good political leader?" she asked in a rare exchange with the media.