The inquiry was apparently launched after a couple of suspicious transactions were reported to tax police in Rome. The Vatican said it would stand by Mr Tedeschi during the investigation.
The Vatican Bank was created during World War II as the bank for religious orders, cardinals, bishops and priests. It is probably best known for the scandal in the early 1980s when Roberto Calvi, known as God’s Banker because of his links with the Vatican, was found hanging under Blackfriars Bridge in London.
The BBC reported that investigators are looking into two suspicious transactions by the Vatican Bank and that one deposit of 23m euros has been seized by the tax police.
The Vatican says it has been working for some time to make its own finances more transparent to comply with anti-terrorism and anti-money laundering regulations.
