The two stores were reported by their local authorities.
"I have also been led to believe that reports are coming in from a further two local councils," said Prosecutor Gunnar Jonasson.
Horrified viewers reacted strongly on Thursday after SVT's Uppdrag Granskning documentary programme showed footage of staff at four large ICA Maxi stores relabeling old minced meat, as well as grinding down other forms of out-of-date meat to make minced meat.
"We have handed in a complaint to prosecutors in which we give our view of the issue," said Daniel Selin, food safety inspector in Nacka municipality, one of the four municipalities to report stores.
"This is unacceptable, and I am surprised that it is so common and happens on such a systematic basis," he said, adding that it was "a clear breach" of the law.
ICA chief press officer Staffan Ekengren said the company had left all the information it had about the stores to the National Food Administration.
"We did this before the programme was broadcast. Our view was that it was important for them to be notified immediately," he said.
"These are large, successful stores which have acted in a completely irresponsible manner," he added.
ICA stores are all owned and operated independently, although operations are coordinated and wholesale operations are run centrally. ICA Sverige AB is half-owned by Dutch retailer Ahold.
ICA quality control managers are to visit the relevant stores at the weekend to hold meetings with those in charge.
"We have had serious conversations with the merchants involved. They are naturally aware that a very major error has occurred," said Ekengren.
Merchants had said "failures in routines and ignorance" were behind the practice. The independent status of the ICA stores means that there are no possibilities of sanctions, but Ekengren said the latest incidents "make it relevant to discuss" whether a system of sanctions could be introduced.