The ruling came as the centre's Trump-appointed board was reportedly scheduled to vote on closing it for two years.
Earlier Tuesday, a federal judge again blocked the board from adding President Trump's name to the facade of the building.
The announcement came after President Trump said he would cancel a $257 million renovation of the venue if his name is not returned to the building.
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National outcry against data center construction has spread to Philadelphia, where officials suggested possible construction in a neighborhood already impacted by a now-defunct oil refinery.
The ruling comes four months after the same judge ordered that the Kennedy Center could not be renamed to include President Trump's name.