Vasovagal syncope is a common form of fainting caused by a sudden drop in heart rate and blood pressure. Sao Paulo said Oscar will undergo further tests.
The Brazilian suffered cardiac complications during pre-season tests on Tuesday and was attended to by club staff and a medical team from Einstein Hospital Israelita, who were at the site.
"Oscar remains clinically well and stable, hospitalised in a cardiology unit, and will undergo an electrophysiological study this Friday," Sao Paulo said in a statement.
Oscar, 34, 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.