As players prepared for pre-season ahead of the 2026 campaign, the club said Oscar "presented a complication with cardiac changes".
The 34-year-old was attended to by club staff and a medical team from Einstein Hospital Israelita, who were at the site.
"The player was then taken to the hospital, where he is clinically stable and remains under observation for further tests to clarify the diagnosis," the club said in a statement on Tuesday.
"In accordance with standard procedure and respecting the player's privacy, new information will be released as soon as there is an update from the medical team, in agreement with Oscar."
Oscar, who won the Premier League twice with Chelsea, spent the majority of his career with Shanghai Port where he won the Chinese Super League twice and became the face of the league that had lured international players with high wages.
He returned to Sao Paulo in December last year, signing a three-year contract with his boyhood club.