Ms Fernandez, 60, has been ordered to rest for a month after doctors discovered bleeding on her brain.
The subdural hematoma was diagnosed as she was undergoing tests for another condition on Saturday.
The diagnosis means Ms Fernandez will have to suspend campaigning ahead of congressional elections.
Cristina Fernandez's health has been followed closely since the sudden death of her husband, former president Nestor Kirchner, from a heart condition in 2010.
She has been admitted to hospital on a number of occasions while serving as president. She has low blood pressure and had to have a thyroid gland removed in 2012.
It is still unclear how her leave will affect congressional elections on 27 October.
While her party has done well in the primaries on a nationwide level it has failed to win a key seat in the province of Buenos Aires, where her rival and former cabinet chief Sergio Massa beat Ms Fernandez's candidate.
Regional heads have however wished the president a quick recovery.
Brazilian President Dilma Rousseff expressed her solidarity with Ms Fernandez on her Twitter account. "Cristina is a friend of Brazil and a friend of mine", she tweeted.
Venezuelan leader Nicolas Maduro wished her a speedy recovery and said that the Venezuelan people would say "loving prayers for the president.”
"From Venezuela, all our love and wishes for a quick recovery; may God bless you and accompany you always!" he wrote.
Colombian President Juan Manuel Santos sent an "affectionate greeting".
It has not yet been officially announced whether Vice-President Amado Boudou, who is facing a corruption investigation, will be in charge of the country during her leave.
In Argentina, politicians of all parties also expressed their support for the president.