The agency wants to examine him in connection with a Foreign Investment Promotion Board (FIPB) clearance given to media group INX Media for receiving funds from Mauritius when his father P Chidambaram was the Union Finance Minister.
It is alleged that a firm "indirectly controlled" by him received money from INX Media, run by Indrani and Peter Mukerjea.
The CBI had issued a notice to Karti to appear for questioning in June but he had sought more time. Later, a look out circular was also issued against him to prevent him from leaving the country, CBI sources said.
During a hearing before the apex court, Karti had told the court that he was willing to appear before the CBI to which it directed him to appear on August 23.
A bench comprising Chief Justice J S Khehar and Justice D Y Chandrachud allowed Karti to be accompanied by a lawyer at the CBI headquarters during the questioning.
The CBI had registered the case on May 15 against Karti, his company Chess Management Services, INX Media, Advantage Strategic Consulting Services, its director Padma Vishwanathan and the Mukerjeas.
The Mukerjeas, charged with the murder of Indrani's daughter, Sheena Bora, are currently in jail.
FIPB approval was granted in "hundreds of cases", the senior Congress leader had said.