The tweet suggested that the son of President Donald Trump should be ripped from "his mother's arms and put in a cage with pedophiles," according to the Associated Press.
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Fonda's film Boundaries will be released on Friday as scheduled, Sony Pictures announced. Fonda's role in the film is small, AP reports. Sony also called Fonda's tweet as "abhorrent."
The Trump family also responded to Fonda's tweet, with Barron's older brother Donald Jr. writing that he disagrees with Sony's decision.
"The tweet is sick and irresponsible," Melania Trump's spokeswoman, Stephanie Grisham, said via email.
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Fonda, a two-time Oscar nominee, who is the brother of Jane Fonda and son of Hollywood legend Henry Fonda, wrote in his apology that he was upset about children being separated from their parents at the U.S.-Mexico border.
Here is his statement, released by both his manager and his publicist:
"I tweeted something highly inappropriate and vulgar about the president and his family in response to the devastating images I was seeing on television. Like many Americans, I am very impassioned and distraught over the situation with children separated from their families at the border, but I went way too far. It was wrong and I should not have done it. I immediately regretted it and sincerely apologize to the family for what I said and any hurt my words have caused."
The Associated Press contributed to this report.