Evangelos Marinakis is being prosecuted for "possession and trafficking of drugs" and for "associating with criminals", a source in the judiciary said on Friday.
Prosecutors in Piraeus, where Olympiakos are based, have also banned Marinakis from leaving the country because of a probe into the financing of a company that chartered the Noor1, a petrol tanker that was seized off the Greek coast in June 2014 with two tonnes of heroin on board.
The heroin was to be transported by truck through Greece and on into western Europe.
Marinakis, 50, has furiously denied the charges.
He bought Nottingham Forest, the two-time European champions who are now in the second tier of English football, in May 2017 in a £50 million ($70.6 million, 57 million euros) deal.
The Greek football league is currently suspended after the owner of PAOK, Greek-Russian businessman Ivan Savvidis, invaded the pitch at the end of a match with fellow title contenders AEK with a holstered gun on his belt.