Sgt Mark Prendeville was taken to the Queen Elizabeth the Queen Mother Hospital in Margate, Kent, after an accident during a training exercise.
A member of staff moved him so other patients could not see the 38-year-old.
A previous "altercation" involving a man in uniform led to the sergeant being moved, the hospital said.
The aircraft engineer needed medical attention after chemicals from a fire extinguisher got into his eyes while training at RAF Manston, Kent, on Wednesday.
Sgt Prendeville was asked to move from the hospital's main waiting area into a different part of the accident and emergency department by a female member of staff, out of the view of the public.
The hospital told the BBC he responded warmly to this proposal.
But Sgt Prendeville's father, Jim Prendeville, told BBC Radio 5 live the treatment of his son was "shameful".
"To say I was incensed would put it mildly.
"He's a very quiet man he didn't want to make a lot of fuss.
"He was more upset by the way he was treated because of his uniform, than he was about the burns in his eyes," he said.
Sgt Prendeville has served in Afghanistan, Bosnia and Iraq, and he was wearing his combat uniform when he arrived at the hospital.
A spokesman for East Kent University Hospitals NHS Foundation Trust said: "A member of the armed forces in uniform attended our A&E and was asked by a member of staff if he wanted to sit inside the department rather than the waiting room.
"This employee was acting in good faith because previously, there had been an altercation between a member of the public and a different member of the armed forces in uniform."
The spokesman also said the hospital trust was "absolutely clear that members of Her Majesty's armed forces, whether in uniform or not, should not be treated any differently to any other person".
"We are now making this point clear to all our members of staff and will seek to make sure that this never happens again," he added.
A hospital has apologised after an RAF sergeant was moved away from other patients because staff said his uniform might cause offence.