The singer, whose mother came to Britain from the Philippines to train as a nurse, made the comments on Twitter yesterday.
The TV star wrote: "To the person who mugged my 67 year old mum and my sister. I hope you get hit by a bus and die. Slowly."
The message received more than 160 retweets and messages from other celebrities including fellow presenter Kate Thornton, Spice Girl Emma Bunton and actress Martine McCutcheon.
Mother-of-two Klass was herself described as "very shaken up" after she was attacked by a gang in Bermondsey, south London, in 2005.