According to Mega television, one of whose senior journalists also received a similar threat, the note was sent by an unknown group calling itself 'Popular Avengers'.
The letter to Provopoulos, containing two 7.65-millimetre bullets, arrived with the rest of his morning mail, a police source said.
Greece's anti-terrorist squad has opened an investigation into both cases.
Provopoulos is currently facing criticism for allegedly lax oversight of Hellenic Postbank, the former state lender whose leadership is under investigation for issuing unsecured loans prior to its privatisation last year.
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According to investigation files published in the press, many of the beneficiaries -- including prominent businessmen -- used the loans for personal enrichment.
Among those being investigated is the head of the Hellenic Financial Stability Fund -- tasked with maintaining the stability of the Greek banking system -- Anastasia Sakellariou, who was formerly part of a Hellenic Postbank commercial loans committee.
The Bank of Greece governor insists he took all steps within his power to curb Hellenic Postbank's loan spree, blocking issuances on two occasions and eventually alerting a state watchdog in 2012.