The postponement is because of the lingering snow cover and persistent cold weather.
The courses had been scheduled to open Wednesday, March 19.
The county-run courses are Mohansic in Yorktown Heights; Maple Moor in White Plains; Saxon Woods in Scarsdale; Hudson Hills in Ossining; and Dunwoodie and Sprain Lake, both in Yonkers.
Golfers are advised to check course status on the day of play.
Information about the courses and reservation instructions can be found at westchestergov.com/golf; for Hudson Hills go to hudsonhillsgolf.com.
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