More than six months after the $15 minimum wage went into effect in New York City, business leaders and owners say the increased labor costs have forced them to cut staff, eliminate work shifts and raise prices.

Many business owners said these changes were unintended consequences of the new minimum wage, which took effect at the beginning of the year.

Susannah Koteen, owner of Lido Restaurant in Harlem, said she worries about the impact raising wages could have on her restaurant, where she employs nearly 40 people. She hasn’t had to lay off anyone, but the increase has forced her to cut back on shifts and be more stringent about overtime. She said she changes her menu offerings seasonally and raises prices more often since the wage boost.

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“What it really forces you to do is make sure that nobody works more than 40 hours,” Ms. Koteen said. “You can only cut back so many people before the service starts to suffer.”

Ms. Koteen said she shelved plans to move her restaurant to a larger location. That would require her to hire more staff, and she isn’t willing to take the risk with the unpredictability of her business. “You would just have no choice but to cut people at the bottom,” she said.

In June, the city’s unemployment rate was 4.3%, compared with the state’s unemployment rate of 4%, according to the New York State Department of Labor. Both numbers have remained relatively steady during the past year.

New York City’s minimum wage has increased three times for employers with at least 11 employees in the past three years. At the end of 2016, the hourly rate rose to $11 from $9 an hour. In 2018, the minimum wage jumped to $13 from $11 an hour. The rate will increase to $15 an hour for employers with 10 or fewer workers at the end of 2019.

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The current federally mandated minimum wage is $7.25 an hour. Other states have passed $15-minimum-wage legislation, including Massachusetts, California, Maryland, Illinois, New Jersey and Connecticut.

Anthony Advincula, spokesman for Restaurant Opportunities Centers United, which advocated for the $15 minimum wage, said there are other factors beyond higher wages that result in unsuccessful businesses, and owners shouldn’t blame the boost for their struggles.

“Increasing to $15 would reduce income inequality, and the number of individuals living in poverty now is ridiculously high,” he said. “This is not just a business issue, this is a race, gender, pay-equality issue.”

Sarah McNally, owner of McNally Jackson Books, employs 75 people at four shops in Manhattan and Brooklyn. Ms. McNally said she hasn’t cut hours or reduced the number of people she employs to mitigate the increase, but she is working to open two more shops and scale her workload to stay profitable.

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While Ms. McNally said she always has paid her employees at least $5 above minimum wage, January’s increase tightened that gap. “With raising minimum wage to living wage, it feels now like we’re at the bottom of the pay spectrum,” she said. “There’s absolutely no benefit to being a retail business in New York.”

Thomas Grech, president of the Queens Chamber of Commerce, said he has seen an uptick in small-business closures during the past six to nine months, and he attributed it to the minimum-wage legislation.

“They’re cutting their staff. They’re cutting their hours. They’re shutting down,” he said. “It’s not just the rent.”

Lisa Sorin, president of the Bronx Chamber of Commerce, said Manhattan businesses and their customers can afford to pay more to compensate for the wage increase, while those in the surrounding boroughs probably couldn’t. “It’s almost like a whirlwind of keep up or get out,” Ms. Sorin said.

Restaurants and establishments with customer bases with less disposable income are challenged, but all are experiencing changes in customer habits regardless of borough, said Andrew Rigie, executive director of the New York City Hospitality Alliance.

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To mitigate the challenges restaurants face, Mr. Rigie said, local and state government should consider providing tax incentives to owners and preserve the tip credit, which allows restaurants to count some or all of an employee’s tips toward its minimum-wage obligations.

“Many people working in the restaurant industry wanted to work overtime hours, but due to the increase, many restaurants have cut back or totally eliminated any overtime work,” he said. “There’s only so much consumers are willing to pay for a burger or a bowl of pasta.”

This report was originally published in The Wall Street Journal.