Judicial officials said in a statement that the investigation was ordered on Monday, a day after the patient died.
The 59-year-old surgeon and hospital administrator was arrested last week after receiving a payment of €500 from the heart attack victim in an operation monitored by police. He has been charged with bribery and blackmail.
Bribery remains widespread in Greece, which is ranked by the Berlin-based Transparency International watchdog group as one of the most corrupt countries in Europe.
Police said the doctor, who has not been named, was arrested after a relative of the patient handed him €500 in marked bills.
The 67-year-old had been rushed to Evangelismos Hospital in late June after suffering a heart attack which required immediate surgery, his family told media.
The heart surgeon allegedly demanded €1,500 under the table to perform the operation.
He is said to have told the 67-year-old that he would be discharged from the hospital unless the payment was made.
According to the police report, the 67-year-old explained that he could not afford such an amount.
After 18 days of waiting, he agreed to pay a smaller amount that would be handed over to the surgeon by a relative.
He then reported the incident to the police who marked the bills the relative paid over to the surgeon, leading to his arrest.
The 67-year-old was subsequently operated on by a different surgeon.
However, he died in intensive care on Monday after suffering another heart attack.