The cancer is in her thyroid gland but has not spread to other parts of her body, a spokesman said.
Ms Fernandez, 58, recently began her second term as president after a landslide election victory.
Her husband - former President Nestor Kirchner - died last year after suffering a heart attack.
Ms Fernandez will step aside as president for 20 days until 24 January, with Vice-President Amado Boudou taking over.
The cancer was discovered on 22 December during routine medical tests, spokesman Alfredo Scoccimarro said.
The cancer - a papillary thyroid carcinoma - had not metastasised or affected her lymph nodes, he added, and the prognosis was very good.
Specialists say this type of thyroid cancer has a high survival rate if treated early.
The BBC's Daniel Schweimler in Buenos Aires says the announcement has come as something of a shock in Argentina.
Ms Fernandez has been very energetic, passing a number of controversial laws, and has not shown any sign of sickness, our correspondent adds.
Ms Fernandez was re-elected in October by a huge margin and remains extremely popular in Argentina.
During her first term she presided over strong economic growth and implemented a range of social policies to benefit the poor.
The sudden death of her husband Nestor Kirchner in October 2010 brought her a wave of public sympathy.
Ms Fernandez is the latest in a series of Latin American leaders to be diagnosed with cancer.
President Hugo Chavez of Venezuela, Paraguayan leader Fernando Lugo, and former Brazilian President Luiz Inacio Lula da Silva have all been operated on in the past year.
Current Brazilian President Dilma Rousseff was treated for early stage lymphatic cancer in 2009.