The ban means that the 21-year-old, who made six appearances as a replacement in last season's Zurich Premiership, will be out of action until October 3.
McKenzie tested positive for ephredrine in a random drugs test after the Wasps v Northampton Saints match on May 17 after unwittingly ingesting the substance in an over-the-counter supplement.
Wasps will be convening their own disciplinary hearing with the promising front rower and also promised to "implement a thorough review of its internal procedures relating to these matters to ensure that there is no chance of any similar proceedings involving its players in the future".
