Stu Jackson, the NBA's executive vice-president of basketball operations, announced the punishment on Saturday.
Smith appears to have eventually deleted the post but that didn't stop the photo from being passed around the Internet on Friday, earning significant attention that included a mention on the sports website Deadspin.
Smith later posted a message directed to the woman, saying, "Things are being taken (too) far sorry (at)therealtahiry."
Smith said following the Knicks' 119-114 loss at Milwaukee on Friday that he regretted posting the picture. He said: "I just have to be smarter in my decisions."