General manager Remo Stirpe said the restaurant's last day of operations will be June 26.
Stirpe and executive chef Ben Geltzer have owned the Monk for the past 10 months.
"I don't know what to say about the closing of the restaurant," Stirpe said. "We have not been doing any business for the last five years."
Stirpe said recent reports that Capital University was interested in acquiring the Bexley Square shopping center where the restaurant is located and converting it to campus uses helped them reach the decision to close. He said those rumors had also affected the business.
Bexley Mayor John Brennan said he was saddened by the loss of the Monk.
"It is a great restaurant," he said. "I think it has fallen on hard times due to the economy. It is a loss for the community. They tried to keep it afloat for several years."
John Spangler, who has been a customer of the Bexley Monk for years, said he frequented the restaurant when it was called the Blind Monk. Over the past five years he got to know the staff after meeting a blind date at the restaurant.
The date went so well that three months later he asked her to marry him at the Bexley Monk. The chef fixed them a special menu and picked out the wine to celebrate the engagement. Last summer his parents celebrated their 65th wedding anniversary at the Monk.
Spangler said Stirpe was never too busy to check on his customers or sit down and talk for a few minutes. Waiter Mike Ferguson told Spangler the Monk was closing.
"He has been there for 13 years," Spangler said. "He was there when we got engaged."