The governing body said the Danish 32-year-old had returned a positive test for Benzoylecgonine, a metabolite of cocaine, which is prohibited by the World Anti-Doping Code and FFA's anti-doping policy.
The attacking midfielder was tested by the Australian Sports Anti-Doping Authority on Jan. 27.
"Mr Larsen (Ilso) is prohibited from participating in the A-League and all other WADA compliant sports," the FFA said in a statement.
"Mr Larsen (Ilso) now has the opportunity to have his B-sample analysed before FFA takes steps to issue him with an Anti-Doping Rule Violation notice."
Ilso said he was awaiting the result of his B-sample in a media release issued by the players' union, Professional Footballers Australia.
"Until these results are received I cannot make any further comments," he said.
"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."
Adelaide are sixth in the 10-team A-League.
(Reporting by Ian Ransom; Editing by Greg Stutchbury)
