The complaint follows unrest among some shareholders and fans over statements made by Mr Wallace regarding the club's finances at December's annual general meeting.
At that meeting Mr Wallace declined to give details of the club's cash situation following claims the club would run out of money in April. He would only state they had ''sufficient cash to continue to trade in the short term''.
Loans totalling £1.5 million were taken out in February, while Mr Wallace's business review released to the stock exchange on Friday, revealed the club has spent £70 million in two years.
A police spokeswoman confirmed: "We have received a complaint, which is currently being assessed to establish if there is any criminality.
"It is an allegation of a contravention of the Companies Act."
A Rangers spokesman said: "Mr Wallace has no knowledge of a complaint, which if put to the football club, has no grounds.
"The outcome of Mr Wallace's business review published by Rangers on Friday gave a comprehensive overview of the circumstances surrounding his arrival at the club and the financial assumptions made at the time."