By Rancic made the remarks after the 18-year-old star arrived at the Oscars on Sunday (February 22), saying: "I feel like she smells like patchouli oil, or maybe weed."
The Dancing With the Stars contestant accused Rancic of being "ignorant, disrespectful and outrageously offensive" on Twitter.
"There is a fine line between what is funny and disrespectful," she said. "Someone said something about my hair at the Oscars that left me in awe. Not because I was relishing in rave outfit reviews, but because I was hit with ignorant slurs and pure disrespect.
"To say that an 18-year-old young woman with locs 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."
The Disney actress also listed several people who wear dreadlocks, including her father, brother, best friend and little cousins.
She also claimed that there was "already harsh criticism of African American hair in society without the help of others who chose to judge people based on the curl of their hair".
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"My wearing my hair in locs on an Oscar red carpet was to showcase them in a positive light, to remind people of color that our hair is good enough. To me locs are a symbol of strength and beauty, almost like a lion's mane."
Rancic later apologised, but insisted that her comments were not racist. She wrote: "Dear @Zendaya, I'm sorry I offended you and others. "I was referring to a bohemian chic look. Had NOTHING to do with race and NEVER would!!!"
Fashion Police star Kelly Osbourne also tweeted that she has opted to keep out of the feud between her co-star Rancic and friend Zendaya.
I WILL NOT BE DRAGGED INTO THIS! The situation is being rectified like ADULTS by both parties. I hope you can leave it to them & do the same!
— Kelly Osbourne (@KellyOsbourne) February 24, 2015
Zendaya was due to play late singer Aaliyah in Lifetime's biopic Princess of R&B, before dropping out and being replaced by Alexandra Shipp.
She released her debut self-titled studio album in September 2013, featuring the single 'Replay'.
