The victim, a woman in her 80s, was walking down an alleyway off Dunstable Road when she was approached from behind and had her purse stolen, before being pushed to the ground.
She sustained serious injuries.
Police have issued a CCTV image of a man that they would like to speak to in connection with the incident.
He is described as white, in his 30s or 40s, with short dark hair.
He was believed to be wearing a padded dark jacket, light grey jogging bottoms, and trainers.
Acting Detective Inspector Jackie Dadd said: “This was a vicious attack which has left an elderly woman with serious injuries, and we’re keen to talk to anyone who might have witnessed the incident as they could help us solve this crime and prevent whoever did it from committing further offences.”
Anyone with information is urged to contact the Luton priority crime team on 101, text 07786 200 011, or call Crimestoppers anonymously on 0800 555 111.