Football Federation Australia (FFA) made the announcement on Friday after Danish import Ilso returned a positive A-sample for Benzoylecgonine – metabolite of cocaine – on 27 January.
It is prohibited by the World Anti-Doping Code and FFA's National Anti-Doping policy.
Ilso has the opportunity to have his B-sample analysed before FFA takes steps to issue him with an Anti-Doping Rule Violation notice.
"To all my fans, team mates, friends and family. I have been notified by the PFA regarding the Adverse Analytical Finding," the 32 year-old said in a statement via the Professional Footballers Association.
"I am working closely with the PFA regarding my situation and awaiting the results from the B test.
"Until these results are received I cannot make any further comments. I would like to thank the PFA for their support in this testing and frustrating situation.
"To our fans, please ensure the focus is on the team. It is a critical time in our season and they need you most of all."
Former Midtjylland and Fortuna Dusseldorf attacker Ilso joined Adelaide in 2018, and the veteran has scored three goals in 19 A-League appearances this season.