The 34-year-old Brazilian suffered cardiac alterations during pre-season tests on Tuesday and was attended to by club staff and a medical team from Einstein Hospital Israelita.
Extensive evaluations confirmed the diagnosis of vasovagal syncope, a common form of fainting caused by a sudden drop in heart rate and blood pressure.
"Stable and clinically well throughout the entire hospitalization period, the athlete will now follow a medical program of rest for the next few days," Serie A side Sao Paulo said in a statement.
Oscar won the Premier League twice with Chelsea and the Chinese Super League three times with Shanghai Port. He returned to Sao Paulo in December last year, signing a three-year contract with his boyhood club.