"I'd say stick to comedy but you weren't funny enough to avoid cancellation of your Netflix show," he tweeted. "Stay away from politics — no reason to suck at two things."
An unexpected third party then entered the quarrel - actor James Woods, who interjected with a sexual innuendo against Handler.
"Think it's safe to say she has sucked at way more than two things..." the 71-year-old Casino star wrote.
Don Jr seemingly agreed, as he replied to Woods writing: "Solid point...".
Trump's tweet sparked outrage from Twitter users who slammed him for being "misogynistic" and "sexist".
One woman, Emily Brandwin, replied to the tweet tagging his sister Ivanka.
"Hey @IvankaTrump - know you're a champion for women and wanted to make sure you saw this solid sexist #BeBesting," Brandwin wrote.
Her hashtag refers to First Lady Melania Trump's Be Best campaign, which serves to educate against cyber bullying.
Ivanka, however, has called herself a feminist on several occasions, and even branded her father one in 2016.
This isn't the first time Handler and Don Jr have been involved in a Twitter argument.
Last year, Handler tweeted criticising his brother Eric Trump and his wife Lara after they announced they were expecting.
Handler tweeted: "Just what we need. Another person with those jeans."
Within hours Donald Jr lashed out at Handler for being "rude" and using the wrong form of "jeans".
He went on to slam the "liberal elite's hatred" spreading in mainstream media.