The 81-year-old was taken into intensive care at the Argentine Institute of Diagnosis in Buenos Aires on Wednesday, a source from the center told AFP.
He underwent a procedure to drain blood and puss from around his brain. It was the second intervention in a little more than a month, according to Argentine press and those close to Bilardo.
He was the coach when a Diego Maradona-inspired Argentina lifted the World Cup for the second time with a 3-2 victory over West Germany in the final in Mexico.
Earlier in the competition, Argentina had knocked out England thanks to Maradona's infamous "hand of God" goal and his iconic solo effort that is often called the greatest goal of all time.
"I want to thank Bilardo eternally for having inculcated in us respect for the Argentina jersey, what it meant to be an international player, the prestige of wearing this shirt," said Sergio Goycochea, who was goalkeeper under Bilardo at the 1990 World Cup in Italy.
Bilardo was twice hospitalized in 2018, at which time it was reported he was suffering from Hakim-Adams syndrome, a neurodegenerative disease common in men over 60.
A gynaecologist by profession, Bilardo took over as Argentina coach following the 1982 World Cup in Spain and stepped down after losing the Italia 90 final 1-0 to West Germany.
A midfielder during his playing days, notably with Estudiantes and San Lorenzo, he also coached Colombia, Argentine giants Boca Juniors and Sevilla in Spain during a coaching career that lasted more than 30 years.