The punishment was handed out following an FA hearing but the sanction has been back-dated to April 21 – the date of the original suspension – with the remainder suspended for two years.
That means McCarey can now be selected by Wolves to play in competitive fixtures.
“Aaron has maintained all along that he has no idea how the drug entered his system,” head coach Kenny Jackett said.
“Medical and scientific analysis, commissioned by the Professional Footballers’ Association (PFA) on behalf of Aaron, and including a hair follicle test requested by the player himself, also showed that the trace amount was very small and backed up Aaron’s statement.
“However, all of our players are aware of the club and the FA’s policy when it comes to substance abuse, and all are responsible for anything which enters their body.
“So while we have supported Aaron throughout, both he and the club understand and accept today’s sanction from the FA.”
McCarey said: “I can categorically state I genuinely have no idea how the trace of the drug entered my system.
“However, there is no disputing the tests which were carried out and I have accepted full responsibility and I apologise.
“This has been a very difficult time for me and my family, and I intend to learn from this experience and improve myself both as a person and as a professional footballer.”
The goalkeeper has also been handed a fine by the and must also complete a tailored course of education and counselling. McCarey will also be subject to internal disciplinary procedures.