Housing secretary Michael Gove has also decided to take over the plans, rather than letting Leeds City Council make the decision.
The secretary will normally only do this if the application conflicts with national policy in "important ways", or is nationally significant.
With large investment in the scheme so far, airport bosses said they were "not prepared to commit a further uncapped sum over an indefinite time frame" into a public inquiry process when their focus "needs to be" on modernising the airport for the future.
The airport will now turn its attention to developing an extension to the existing terminal, originally approved by Leeds council in 2019.
The replacement terminal plans were initially proposed to help the airport meet demand in a "more sustainable way".
LBA said it remains committed to delivering its 2030 carbon net-zero roadmap and to creating a "modern, decarbonised" regional UK airport within the extension scheme.
Vincent Hodder, chief executive of the airport, said LBA needs to be able to respond to "rapidly increasing demand" within the next few years as travel and aviation continues to recover from the impacts of the pandemic.
"It is with regret that we have made the decision to withdraw LBA’s application for the development of a new replacement terminal," he added.
"I would like to thank everyone who has supported us in the planning process, from the general public to the business community and councils across Yorkshire."