To ease anxious minds, Trump passed the reigns of his businesses to his sons and disbanded his foundation.
Viola, who is worth an estimated $1.8 billion, was reportedly distraught to give up on serving as Army Secretary, but was unable to sell his holdings without harming the companies he helped build.
Viola is also the owner of the Florida Panthers, a National Hockey League team.
All airlines face federal regulations and could prove to be a conflict of interest for a government official.
In a statement to the Military Times, Viola said he was "deeply honored" by the nomination, despite it not panning out.
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A former Pentagon official and close friend of Viola's told theNew York Times that Viola was "devastated" over his decision to not be part of the richest presidential Cabinet in US history.
"Secretary Mattis is disappointed but understands and respects Mr. Viola's decision", a Pentagon statement said, adding that Secretary of Defense Jim Mattis would recommend another candidate soon.
"I appreciate the confidence President Trump showed in me", he said.
Mr Trump has nominated Heather Wilson to take over as Air Force Secretary and Philip Bilden to become Navy Secretary, but confirmation hearings have not been announced for either role.
Viola has now become the first of Trump's nominees for Cabinet positions to withdraw himself from consideration for a post.