The Fashion Police host said that Coleman, who wears her hair in dreadlocks, looked like she smelled of "patchouli oil and weed" at the Oscars.
Coleman responded via her Twitter and Instagram feeds with an open letter, calling the remark an "ignorant slur".
"There is a fine line between what is funny and disrespectful. Someone said something about my hair at the Oscars that left me in awe," the actress wrote.
"I was hit with ignorant slurs and pure disrespect. To say that an 18 year old young woman with locs [dreadlocks] must smell of patchouli oil or 'weed' is not only a large stereotype but outrageously offensive. I don't usually feel the need to respond to negative things, but certain remarks cannot go unchecked."
On Tuesday night, Rancic recorded an emotional apology to Coleman and anybody else offended by her joke. "I'd really like to address something that is weighing very heavy on my heart. I want to apologise for a comment that I made on last night's Fashion Police about Zendaya's hair," she said. "Now, as you know, Fashion Police is a show that pokes fun at celebrities in good spirit, but I do understand that something I said last night did cross the line.
"I just want everyone to know, I didn’t intend to hurt anybody - but I’ve learned it’s not my intent that matters, it’s the result. And the result is that people are offended, including Zendaya, and that is not OK. Therefore, I want to say to Zendaya, and anyone else out there that I have hurt, that I am so, so sincerely sorry. This really has been a learning experience for me."
She added: "This incident has taught me to be a lot more aware of cliches and stereotypes - how much damage they can do, and that I am responsible, as we all are."
The actress was also praised by Selma director Ava DuVernay, who described her as a "beautiful queen".
Rancic's first apology, issued on Tuesday via Twitter, stated that her remark had "nothing to do with race".
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