The complaint follows unrest among some shareholders and fans over statements made by Mr Wallace at the Ibrox club's annual general meeting last December.
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 stated they had "sufficient cash to continue to trade in the short term".
Loans totalling £1.5 million were taken out in February this year, while Mr Wallace's business review, released to the Stock Exchange on Friday, revealed the club had squandered £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.
The Union of Fans is "absolutely appalled" by the developments and says club chairman David Somers should step in to suspend Mr Wallace until investigations into the allegations are complete.
"It is time for Mr Somers, our absent chairman, to step forward and clear up this mess.
"He is responsible for the total lack of corporate governance on this board and must act now or his own reputation with be irrevocably damaged.
"We have consistently stated that his AGM undertaking that the club had sufficient funds was false and nothing that has happened since has shaken us from that belief.
"We are not surprised that his refusal to address this issue has led to angry shareholders taking this action and we hope there will be a thorough investigation.
"This board is a disgrace to Rangers Football Club and the current members of it are running our club into the ground while simultaneously making a mockery of the positions they are privileged to hold."
Amid threats of a refusal by supporters to give season ticket money for the new campaign directly to the club, the club said last week that it is now unable to accept payment for next season by either credit or debit card.
The Union of Fans refuted suggestions that it was the season ticket issue that created the situation.
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."