The move by APA on Thursday comes two days after it raised its offer to A$9.96 billion ($7.22 billion) for the energy infrastructure firm.
The winner of the bidding war will bag the critical Victorian electricity transmission network and related assets owned by AusNet, which counts Singapore Power and State Grid of China as its major shareholders.
APA said it had been unjustly locked out from an opportunity to negotiate with AusNet for at least eight weeks, the duration of the exclusivity period, and sought orders from the panel to terminate the arrangement.
AusNet did not comment as the matter is under investigation by the Takeovers Panel. Brookfield declined to comment.
AusNet said on Tuesday it had rejected a previously undisclosed bid of A$2.32 per share from APA and subsequently granted exclusive due diligence to Brookfield.
The move disappointed APA, which said AusNet knew of an impending revised and potentially superior proposal by the pipeline company.
Analysts at UBS said Brookfield's bid may face scrutiny from the Foreign Investment Review Board on national security grounds because if the proposal goes through, Victoria electricity distribution network would become 100% foreign-owned.
AusNet shares, which have soared more than 30% this week after the bids were made public, closed 2.4% higher on Thursday. APA ended 2% higher.
(Reporting by Riya Sharma and Savyata Mishra in Bengaluru; Editing by Arun Koyyur)