WASHINGTON—The U.S. labor market notched its 100th straight month of increased employment in January while sustaining robust wage growth, passing the tests posed by a federal-government shutdown, market volatility and uncertainty about global economies.

Nonfarm payrolls rose a seasonally adjusted 304,000 in January, the Labor Department said Friday. The gain was well above last year’s average monthly job growth and showed that most private-sector businesses shrugged off the shutdown and kept on hiring.

Wages...