The tweet, which was posted during the inauguration and referred to President Donald Trump's son as the person who would be "this country's first homeschool shooter," was met with condemnation and has since been deleted.
Although NBC has not commented, a source familiar with the situation tells TVGuide.com that Rich was suspended immediately after her tweet and the suspension is indefinite. Rich's name was also not in the credits of Saturday's show, which was hosted by Master of None's Aziz Ansari.
On Monday, Rich released a public apology via Twitter.
"I sincerely apologize for the insensitive tweet. I deeply regret my actions & offensive words. It was inexcusable & I'm so sorry," she wrote.