Two hours after Mayor Bill de Blasio unveiled what he described as a “game changer” in affordable housing — an ambitious plan to build an 11,250-unit development on top of active rail yards in Sunnyside, Queens — Gov. Andrew Cuomo said the yards are not available.

The mayor made the proposal in his second State of the City speech, an 80-minute address focused on expanding housing for the poor and middle-class.

The Sunnyside Yards were a key component of the mayor’s plan.

But Cuomo said the yards are already spoken for.

“The [Metropolitan Transportation Authority] uses Sunnyside Yards as an important facility for our transportation system, and it is not available for any other use in the near term,” Cuomo’s spokeswoman, Melissa DeRosa, said in a statement.

“The state and the MTA are studying several potential future uses of the site from a long term planning perspective.”

Cuomo has considerable sway with the MTA; he appoints its chairman, with state Senate approval.

The burgeoning tug-of-war is just the latest hurdle for the 202-acre plot, which had a number of proposals derailed in recent years — often because of the prohibitive cost of building a deck over the active rail lines.

City Hall has yet to release details of the proposed development, but officials noted that Amtrak owns 113 of the acres, 23 acres are privately owned, and the MTA owns the remaining 66 acres.

Of the MTA’s portion, the city owns air rights over 44 acres — which means it has the legal right to build there as long as train service isn’t disrupted.

Despite Cuomo’s swift rebuff, City Hall spokesman Wiley Norvell said officials were still planning to move to turn the proposal into reality.

“As the mayor indicated in his address, our feasibility study will constitute an exhaustive process undertaken with local stakeholders to activate the Sunnyside Yards while continuing their role as a vital link in the region’s rail system,” he said. “We have engaged the MTA and Amtrak to ensure that any development prioritizes their transit operations.”

Cuomo also hit back at de Blasio’s call for the minimum wage to be set at $13 per hour in New York City, just weeks after the governor himself called for the rate to be hiked to a lower $10.50 statewide, and $11.50 in New York City.

The current minimum wage is $8.75 per hour across the entire state.

“The governor agrees with Mayor de Blasio that we must raise the minimum wage in New York,” said DeRosa. “While we believe the state Legislature will view an increase to more than $13 as a non-starter, we will continue to push for the aggressive proposal the governor outlined last month that also accounts for the higher cost of living that workers experience in New York City.”