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.
A map showing the location of Chile
Former Chilean President Augusto Pinochet, 91, has suffered a heart attack early this morning. His son, Marco Antonio, declared that his father had received his last rites from a Catholic priest and that "he is in the hands of God and the doctors". Pinochet underwent a bypass surgery in the Hospital Militar in Santiago and his condition is reported to be critical but stable. Doctors have reported he is also suffering from pulmonary edema. 

Pinochet came to power in 1973 when the Chilean armed forces led a coup which deposed the left-wing president Salvador Allende. Allende's rule had seen a growing polarization of Chilean society, economic crisis, and terrorist activity from far-left groups. Pinochet set about exterminating his opposition, mainly socalists and communists, and suspended the constiution. His neoliberal economic policies, carried out by the "Chicago Boys", a group of Chilean economists influenced by Milton Friedman, were able to reduce the rampant hyperinflation and stabilize the economy. In 1981, a plebiscite approved a new constitution drafted by Pinochet's government. As the new constitution decreed, another plebiscite took place in 1988 to determine whether Pinochet should remain in power. The "No" option won and Pinochet stepped down. He remained as head of the army and senator until 1998, when he relinquished these positions. He was arrested that year in London for human rights violations, but was able to return to Chile. He is currently under investigation by Chilean officials over tax evasion and human rights violatons. He had recently accepted "responsibility" for "everything that was done" during his government, "which had no other goal than making Chile greater and avoiding its disintegration".