Arsen Avakov said in a Facebook post a criminal case had been opened against Mr Yanukovych and other officials over "mass murder of peaceful citizens".
MPs voted to remove Mr Yanukovych on Saturday after months of protest sparked by his rejection of an EU deal.
A crackdown on the protests last week left dozens dead.
Mr Azakov said Mr Yanukovych was seen in Balaklava on the Crimean peninsula on Sunday, but that he had left by car for an unknown destination, accompanied by an aide.
Before leaving Balaklava he had relieved his security detail of their duties, said the statement.
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