Images of the fire were posted to social media on Monday night.
The Cornwall Office of Emergency Management said winds were spreading the flames around 7:30 p.m.
Breakneck Mountain is a popular area for hiking and getaways from the city.
The fires have jumped Route 9D, closing the road between Cold Spring and Dutchess Junction.
The cause of the fire is not yet known.
Few other details were released.
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