Maradona's family transferred him on Sunday from an intensive care ward where he was treated for heart and lung problems to the Clinica Privada for drug addiction treatment on the outskirts of the capital.
"We have to preserve him as an idol, but we must think in human terms ... I get the impression that this is the last chance we have," his personal doctor Alfredo Cahe told reporters.
Cahe said his treatment would take "a very long time."
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While on a visit to Argentina last month, Maradona was rushed to hospital with a swollen heart and breathing problems and he spent two weeks in intensive care, including a week on an artificial respirator.
After a slow recovery, he suddenly discharged himself and hours later played night-time golf with glow-in-the-dark balls. Days later he was taken back to hospital in an ambulance with breathing problems.
The clinic said on Monday that Maradona's health was stable.
Maradona's reputation for being a difficult patient led many clinics to refuse to admit him, worried about the media entourage and noisy fans who follow his every move.
The Clinica Privada, situated in a wooded area, was heavily guarded by police and private security. Only hours after his arrival on Sunday, small groups of onlookers and fans gathered nearby, some hanging "Get Well" messages on a gate.