One of New York City Mayor Bill de Blasio’s signature initiatives hit an obstacle this week, when Gov. Andrew Cuomo’s administration curbed a financial resource critical to building low-income housing.

The city expected to receive the authority to issue more than $200 million in tax-exempt bonds for affordable housing projects. But city officials were told this week that they wouldn’t be getting any further issuing authority this year, according to three people briefed on the issue.

While...