The writer, Katie Rich, fired off a tweet targeting the 10-year-old boy, which read, "Barron will be this country's first homeschool shooter."
The writer was quickly suspended by the popular American TV show after the post, reported Entertainment Weekly.
Rich, however, deleted the tweet hours later and posted an apology via another tweet.
"I sincerely apologise for the insensitive tweet. I deeply regret my actions and offensive words. It was inexcusable and I'm so sorry."
As Barron was subjected to taunts from internet bullies for looking bored during his father's inauguration, he found unlikely support from Trump's rival Hillary Clinton's daughter, Chelsea, who jumped to the young boy's defence.
"Barron Trump deserves the chance every child does -- to be a kid," Chelsea posted on Facebook.
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