"The recent virus has visited me and I felt obliged to let the public know," Marinakis said in an Instagram post.
"I feel good, as I take all the necessary measures and I discipline to the doctors' instructions. I strongly advise all my fellow citizens to do the same. I wish all a quick recovery."
In a statement, Nottingham Forest revealed that Marinakis - who was present at the team's home stadium, City Ground, last Friday - began to show symptoms on Monday afternoon in Greece.
"Mr. Marinakis was diagnosed after showing the first symptoms on his return to Greece yesterday afternoon. During his short stay in Nottingham last week he did not show any symptoms of the virus," the statement read.
"The club is seeking advice from medical professionals and the relevant governing bodies to ensure the correct measures are taken. Until this time the club will be making no further comment."
The 52-year-old Marinakis was also present at the Emirates Stadium in north London on Feb. 27 to watch Olympiacos knock Arsenal out of the Europa League.
Arsenal have since issued a statement confirming that players and staff members who came into "close contact" with Marinakis have begun self-isolation. The news resulted in the Premier League postponing Wednesday's fixture between Manchester City and Arsenal.
"The players will remain at their homes until the 14-day period expires. Four Arsenal staff, who were sitting close to Mr Marinakis during the match will also remain at home until the 14 days are complete," the statement read.
UEFA rejected Wolverhampton Wanderers' plea to postpone Thursday's match at Olympiacos, therefore keeping the fixture behind closed doors.
"Our position is that the trip poses unnecessary risks to our players, staff, supporters and the families of all who travel, at such critical and uncertain times," Wolves said in a club statement.