More than three weeks on from the terrifying incident, police have not been able to locate or identify the offender, described as being caucasian or of mixed race, in his early 20s, about 160cm tall, with a slim build and tanned skin.
He was "dirty and shabby in appearance".
McKay said the offending was "random" and "bizarre", but that there had been no reported incidents in the weeks since it has happened, so police believed it to be isolated.
In a post on Facebook, a woman believed to be the victim said she had experienced a "serious violent home invasion".
She said a man dressed all in black and wearing a black hoodie "barged" into her and slashed at her arm with a knife.
"He didn't get in and then ran," she wrote.
Anyone with information on the incident is urged to contact police, or contact Crimestoppers anonymously on 0800 555 111.