Gen Pinochet celebrated his 91st birthday a week ago
The 91-year-old needs a second intervention, state media has reported medics treating him as saying.
The former leader, who was put under house arrest a few days ago, is in a military hospital in Santiago.
Gen Pinochet was in power from 1973-90, during which time more than 3,000 people were killed or "disappeared".
He is accused of dozens of human rights violations but has never faced trial because of poor health.
Angioplasty procedure
He was taken to hospital early on Sunday morning after suffering "an acute" heart attack and a build-up of fluid on his lungs, a statement from the hospital said.
Doctors had carried out "procedures that rescued him virtually from death," Gen Pinochet's son, Marco Antonio Pinochet told reporters gathered outside the hospital.
"He's in a pretty serious state...We're in the hands of God and the doctors."
The former leader received the last rites from a Catholic priest, a family spokesman said.
One of the medical staff, Dr Juan Ignacio Vergara, said Gen Pinochet was in a stable condition but his life was not out of danger.
Gen Pinochet underwent angioplasty, a procedure designed to widen a narrowed or totally obstructed blood vessel, to stabilise his condition, he said.
Now, according to reports on Chilean state television, he needs a second operation - possibly a heart by-pass.
'Political responsibility'
General Pinochet overthrew the elected government of the left-wing President Salvador Allende in 1973 in a bloody coup.
He was placed under house arrest earlier this week over the abduction of two people in 1973.
The charges relate to the Caravan of Death - a military operation to remove opponents to Gen Pinochet's rule.
He currently faces two other indictments - one for human rights abuses and another for tax evasion.
As a former president he enjoys legal immunity, but the courts can strip him of this privilege on a case-by-case basis.
On 25 November, his 91st birthday, Gen Pinochet issued a statement in which he took "political responsibility" for acts that took place under his rule, saying that he had believed they were in Chile's best interests.
He also alluded to his failing health.
"Today, close to the end of my days, I want to make clear that I hold no rancour toward anybody, that I love my country above all else," he said.
Gen Pinochet has been in ill health in recent years. He suffers from diabetes and arthritis, and has also had a number of suspected strokes.
Localisation du Chili 
L'ancien président du Chili, le général Augusto Pinochet, 91 ans, a eu une attaque cardiaque tôt ce matin. Son fils, Marco Antonio, a indiqué que son père avait reçu l'extrême onction d'un prêtre catholique et . Pinochet a été mis sous assistance cardiaque à l'hôpital militaire de Santiago et l'équipe médicale a indiqué que son état était critique mais stable. Outre son arrêt cardiaque, les médecins ont dit qu'il avait aussi eu un œdème pulmonaire.