The decision makes it unlikely that Airbnb will be embroiled in a drawn-out legal battle over whether the company is responsible when hosts discriminate against guests based on their race, religion, gender or other factors.

Mr. Selden plans to appeal the judge’s decision, said his lawyer, Ikechukwu Emejuru.

“By placing Mr. Selden’s claims into arbitration, a consumer’s constitutional right to a jury trial and access to the courts of law continues to be whittled down gradually but surely,” Mr. Emejuru said in a statement.

Airbnb has been grappling with the issue of discrimination on its service for months. Last December, a working paper by Harvard University researchers found it was harder for guests with African-American-sounding names to rent rooms through the site.

While it is illegal for hotels to turn away guests based on their race or other factors, Airbnb hosts have typically had more leeway in terms of whom to rent to. The company has worked to narrow that wiggle room. In September, it took several actions to combat discrimination, including requiring hosts to agree to a “community commitment” starting on Nov. 1 and hewing to a new nondiscrimination policy.