South Korea had hoped Leverkusen would release the 22-year-old for the latter stages after the German side denied their initial request for him to participate in the entire tournament.
The Korea Football Association (KFA) said earlier on Wednesday it had asked Leverkusen to free Son for the last 16 but later announced that request had also been rejected.
"The KFA has decided not to include Son Heung-min for the Asian Games," it said in a statement.
"The association officially asked the team to release Son during its visit to South Korea but in a reply sent yesterday evening it said Son is an important player for the team and cannot release him due to the upcoming Champions League.
"In response, the KFA asked the team to release him for the last 16 but Leverkusen declined, saying they cannot release him for a tournament that is not part of FIFA’s official calendar."
The Asian Games football tournament is not part of world football's governing body FIFA's official calendar so club sides are under no obligation to release players to take part.
Leverkusen visited Korea in July and played a friendly against FC Seoul.
Son, 22, left Seoul's Dongbuk High School as a 16-year-old to join Hamburg SV's youth academy and has flourished in the Bundesliga. He moved to Bayer Leverkusen for a fee of 10 million euros (7.95 million pounds) last year.
Son was one of the few players to emerge with any credit from South Korea's woeful World Cup campaign in Brazil, scoring against Algeria in a 4-2 loss in Porto Alegre.
South Korea won the bronze medal at the last Asian Games in 2010. They have won gold three times - twice in Bangkok, in 1970 and 1978, and in Seoul in 1986.
The KFA will hold a news conference on Thursday to announce the Asian Games squad, with Lee Kwang-jong, who is coaching the football team at the tournament, set to speak to the media.
The Games will be held in the South Korean city of Incheon, west of Seoul, and run from Sept. 19 to Oct. 4.
(Reporting by Narae Kim; Writing by Peter Rutherford; Editing by Nick Mulvenney)
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