Vicky Stamati, married to Socialist Party stalwart Akis Tsochatzopoulos, disappeared early on Thursday morning.
The window latch of the room where she was being treated in Athens was broken, Greek media reported.
Stamati was sentenced to 12 years in 2013 for money laundering.
Known to be in poor health, she endured a double mastectomy shortly after her trial.
She was transferred to the psychiatric hospital in December 2013 after reportedly suffering a breakdown, attempting suicide and being diagnosed with severe depression.
Stamati has appealed five times to be released from prison, citing her poor health and the fact that her young child is now being brought up by her elderly mother. But all appeals have been rejected.
Police say they are concentrating their search for Stamati in Athens.
An investigation has been launched into the circumstances of her dawn escape from a guarded cell in the Dromokaitio state psychiatric institution.
The facility's director, Pavlos Theodorakis, told Protothemanews.com that she may she have been helped to leave - possibly via a balcony.
Tsochatzopoulos served as defence minister from 1996-2001 and was one of the most influential men in the powerful socialist Pasok party. His trial was one of Greece's biggest corruption cases in decades.
The minister was found guilty of pocketing bribes paid through offshore companies for the procurement of a Russian rocket defence system and German submarines.
He was sentenced to 20 years in prison and is currently appealing against his conviction.
Stamati was convicted on the basis that she knew about the bribes her husband accepted.
A former Greek defence minister's wife,  jailed for corruption, has escaped from a psychiatric hospital where she was serving her sentence.