Police confirmed they had shelved a complaint about comments made to a Rangers annual general meeting last December.
Phil Maher, an Ibrox shareholder, claimed Mr Wallace insisted the club had enough funds in place to operate until May. Two months later the board took out a £1.5million emergency loan.
Dismissal of the complaint comes a month after it emerged Rangers would face no further police action over alleged failures in corporate governance made by another shareholder.
The Ibrox club had been facing a police investigation after another shareholder, Billy Paterson, reported the club because he was unhappy it had refused to provide contract details for former chief executive Charles Green and former commercial director Imran Ahmad.
Police said they would be taking no further action in response to Mr Paterson's complaint, saying "no criminality was established".
The force had also been assessing Mr Maher's complaint, and whether there was any criminality through a breach of the Companies Act.
A spokeswoman confirmed: "Police Scotland will not be conducting a criminal investigation at this stage into the matters raised by Mr Maher."
Rangers officials, who always insisted the complaint "has no grounds", were unavailable for comment.
When making his complaint banker Mr Maher said: "As a shareholder and lifelong Rangers fan, I am appalled at the financial mismanagement we continue to witness and extremely disappointed that I have felt the need to take this course of action."
His complaint led to calls from the Union Of Fans, an umbrella organisation that comprises the main three supporters' groups, for the club to suspend Mr Wallace while the matter was cleared up.
Many of the club's officials were booed and jeered at the Rangers International Football Club plc AGM, which was held in the open air at Ibrox on December 19 and attended by almost 2000 shareholders.
Opposition shareholders failed to appoint ex-chairman Malcolm Murray, former oldco director Paul Murray, property adviser Scott Murdoch and former human resources director at BT Alex Wilson as directors of RIFC plc.
Current chairman David Somers, chief executive Graham Wallace and three directors were all re-elected. Mr Wallace won the greatest amount of support with 85.5% in favour.
Finance director Brian Stockbridge bore the brunt of fan fury for presiding over losses of £14.3 million while taking a salary and bonus package of about £400,000.
Mr Stockbridge, who left the club in January, was booed every time he spoke. On Tuesday it emerged he had received shares in the club worth about £215,000 under a deal made when he joined the board along with Charles Green.
Mr Wallace's business review blamed the club's financial predicament on the way that previous boards spent all of the £70m raised in two tranches of season ticket sales and the launch of RIFC on the Alternative Investment Market.
Legal advisers for Rangers had said Mr Paterson's complaint was time-barred in that they needed to show only service contracts for the previous 12 months.
Club sources explained Mr Green's and Mr Ahmad's "service contracts" were ended in April 2013, and were "outside the one-year inspection period stipulated by the legislation".
Mr Paterson, 49, of Fraserburgh, insisted Mr Green and Mr Ahmad were still officially recognised as directors of the parent company and the subsidiary football board until the end of last May.