Kelly, 29, is believed to have reacted to Katie's comments about her mother Sharon Osbourne, in which she criticised the X Factor judge's love of plastic surgery.
"Sharon reckons her time on the panel may be up," wrote Katie in her column for Best. "Either way, if she is going to look this good next year she will need to bulk buy plastic."
Sharon and Kelly Osbourne
Quick to jump to her mother's defence, Kelly lashed out on Twitter — and she didn't mince her words.
"@KTHopkins U R a hypocritical vile human that is addicted 2 attention U R so insignificant! Don't you ever talk about my mother again! #India," wrote Kelly to her 3.5million followers. The hashtag is thought to be a reference to Katie's young daughter India.
Mother-of-three Katie, who publicly clashed with Peaches Geldof on This Morning about attachment parenting, responded to Kelly's tweet, writing, "Just like Peaches and Jesus, Kelly has done well due to a famous parent. @KellyOsbourne."
The argument didn't stop there, with Kelly and Katie firing a string of insults back and forth.
"@KTHopkins just like you can't help the parents you came from neither can I! I don't see you on a @Forbes list I work my bum off nice try...," said Kelly, writing in another tweet, "I feel sorry for you & Ur ignorance!"
"Actually made my night that @KTHopkins considers herself a lady when I think of her a desperate sad old bitter child is what comes to mind," added Kelly.
"No problem Kel. No one ever mistook you for a lady sweetie pie.@KellyOsbourne," responded Katie.
The outspoken former Apprentice contestant has become well known for her controversial — and often confrontational — views. Katie made waves with her opinions on overweight children, school mums and red-haired children and most notably when she said she judged children with "lower class names".
"I think you can tell a great deal from a name," said 38-year-old Katie. "For me, there's certain names that I hear and I think 'urgh'. For me, a name is a shortcut of finding out what class a child comes from and makes me ask, 'Do I want my children to play with them?'
"When I hear screeched across the playground, 'Tyler! Come back 'ere.' It's the Tylers, the Charmains, the Chantelles, the Chardonnays…
"There's a whole set of things that go with children like that, who are quite a disruptive influence in school and that's why I don't like those kind of children," she added.