Lieutenant-general Solly Shoke said that the Army was in consultation with the surgeon-general over the matter.
"I hope they will take the nature of our job into consideration," he told reporters in Pretoria.
Shoke's argument was that Army troops needed to be mentally and physically fit to perform their duties, which often landed them in extreme conditions.
He said that deploying an HIV-positive person into a hazardous situation could threaten the person's life.
"We view the judgement in a very serious light," stated Shoke. "It should be common knowledge that, in order to fulfil our operational requirements, the implication is that soldiers with the right physical and psychological makeup are required."
He said that in any organisation, jobs had certain criteria that needed to be met.
Shoke went on to lament that the court application against the army focused solely on HIV, while the Army considered a comprehensive health assessment, "which implies we check everything".
Daily newspaper Pretoria News reported on May 17 that the South African National Defence Force's defeat came after its admission that its policy preventing HIV-positive people from being recruited, deployed or promoted was unconstitutional and discriminatory.
The SANDF's lawyers agreed that the matter be settled in favour of the South African Security Forces Union before even arguing their case, the paper said.
The SANDF now had to come up with a new health classification and testing policy by November, to which end it had engaged the surgeon general.
Shoke said that the South African Army would obtain "legal advice" on the matter.