The 32-year-old was an ever-present in the Pakistan line-up during the global tournament, playing seven matches while taking seven wickets and scoring just 15 runs.
The ICC have yet to formally make any announcement about the positive test but the Pakistan Cricket Board (PCB) have commented.
A PCB spokesperson told ESPNcricinfo: "The International Cricket Council (ICC) has informed the Pakistan Cricket Board (PCB) about this matter, and PCB has begun the due process. The results of this process will be communicated to the ICC today."
Nawaz has played for the Multan Sultans in the ongoing Pakistan Super League season.
The left-arm spinner had been due to join English county side Surrey for the T20 Blast next month but that deal has now fallen through.
Pakistan have appointed former captain Sarfaraz Ahmed as new head coach and also selected four uncapped players in the squad for the Test series in Bangladesh next month.
Saim Ayub and Babar Azam have been dropped while six uncapped players have been selected for Pakistan's ODI squad for the three-match series against Bangladesh.
Pakistan captain Salman Agha said his team fell short in too many key moments at the ICC Men's T20 World Cup after they played their final game against Sri Lanka on Saturday.
Pakistan missed out on qualification to the T20 World Cup semifinals despite a thrilling five-run victory against co-hosts Sri Lanka in Pallekele on Saturday.
