Nam, world No 475, lost to Zhizhen Zhang of China, world No 716, 6-4, 6-4 in the event’s second round.
Earlier, No 8 seed Nam crushed Sheng Hao Zhou of China 6-4, 6-2 in the first round.
With this result, Nam, a Tay Ninh Province native, will add only one ranking point to his total.
Nam will next compete in the China F12 Men’s Futures tennis tournament on July 10-16. He is the No 9 seed.
Nam, 20, is one of the top 32 players in Asia. In Southeast Asia, he ranks only behind Christopher Rungkat of Indonesia, who is 463rd in the world.