The reigning champion was playing in just his third match in a year after a career-threatening wrist injury and suffered a shock 7-6 7-6 defeat to the world No 66.
Neither player???s serve was broken during the quarter-final tie, and Kukushkin frequently targeted Del Potro???s backhand to test out his troublesome wrist.
The Argentine had entered the tournament as a wildcard after beating Bernard Tomic in last year???s final as a warm-up for the Australian Open.
Del Potro had previously seen off Ukraine’s Sergiy Stakhovsky and Italy???s Fabio Fognini.