The 24-year-old woman was slashed in the right side of her neck, right hand and right leg at 63rd Street and Center Drive just after 1:30 p.m.
She was taken to New York Presbyterian Hospital with non-life-threatening injuries.
The suspect fled on foot through Heckscher Park, accompanied by her husband and son.
Detectives said the two are food vendors involved in an ongoing dispute over their territory in Central Park.
In their last altercation on Christmas Eve, Tuesday's victim was the aggressor.
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