The iconic restaurant, filled with memorabilia and photographs of the late Wendy's founder, Dave Thomas, will close March 2.
"This is a very difficult decision, but the truth is we kept it open for sentimental reasons much longer than we should have," company spokesman Denny Lynch said.
Thomas, who died in 2002 of liver cancer, opened his first Wendy's Old Fashioned Hamburgers on Nov. 15, 1969. He named the restaurant after his 8-year-old daughter, Melinda Lou, nicknamed Wendy. He later became a nationally known figure as a Wendy's pitchman in television commercials.
But the original restaurant, just a few blocks from the Ohio Statehouse, is unable to generate sufficient sales at night or during weekends, when government buildings are closed, Lynch said.
The restaurant has no drive-through window, has limited parking and soon would have required substantial building improvements, Lynch said. No sales figures were released.
Thomas knew before he died that his first restaurant was struggling, Lynch said.
"I guarantee he would support this decision," Lynch said. "He recognized that a company needs to be profitable."
Employees will be offered jobs at other locations, Lynch said. The company hasn't decided whether it will hold a closing ceremony.
"It's sad to see history disappear," said Mark Barbash, the city's director of development. Wendy's owns the building and the land, and city officials hope to meet with the company to discuss redevelopment ideas.
Memorabilia at the restaurant, including the dress worn by Thomas' daughter when she posed for the restaurant's logo, will be moved to the company's corporate offices in Dublin, a Columbus suburb.
Wendy's operates about 6,600 restaurants in the United States and abroad.