Officers were called to the Overgate Centre in Dundee following the incident where the unknown woman appeared to push the 18-piece dinner set from the top floor narrowly missing shoppers.
Centre bosses then say that the woman casually walked back to her car before driving out of the multi-storey car park — smashing through the closed exit barrier to get away.
The set had been bought earlier that day in Argos.
City centre councillor Ken Lynn condemned the women’s actions, which he said could have killed a passer-by.
He said: “If she has deliberately thrown it and then driven right through the barrier then there is something strangely malicious about what happened.
“Doing that is one of the most dangerous things I’ve ever heard of — that could have seriously hurt someone or killed them.
“I can’t work out the motivation behind it, but the police need to track her down so she can be prosecuted or given help.
“Hopefully the Overgate will have CCTV in certain places so they can identify her.
“I’d also urge anyone who witnessed it to come forward with any information.
“It’s not the sort of thing you would forget in a hurry.”
Centre manager Malcolm Angus reassured customers that nobody had been injured.
He said: “There was an incident in the Overgate on January 7, when a customer dropped a boxed 18-piece dinner set from beside Millies Cookies to the lower level
“Thankfully, the box didn’t hit any customers.
“The lady then proceeded east along the mall and exited the centre via the car park.
“We are liaising with Police Scotland to identify the lady in question to try to understand her actions.
“We can rest assure all our customers this is an isolated incident and we, at all times, have customer wellbeing at the forefront our customer care.”
A spokeswoman for Police Scotland confirmed that officers were investigating.
She said: “We are making inquiries into an incident at the Overgate that happened at about midday on January 7.”
She added that nobody had been charged in connection with the incident.