'Police officers apprehended and transferred the convict to prison,' the Tehran prosecutor's office said, cited by the Fars news agency.
Baghai was sentenced in December to 15 years in prison for embezzlement and illegal business transactions.
Baghai, 48, is very close to Ahmadinejad, serving as his deputy before becoming chief of staff during the former president's second term.
Baghai was briefly detained in 2015 on corruption charges.
The powerful Guardians Council prevented him from running in the May 2017 presidential election, and he was jailed for a few weeks in July.
Based on reporting by AFP and Fars