Gates, 57, might have not realized it Monday, but a one-hand shake in Korean culture - and also in Asia - is notably casual, done only when the other party is a good friend, of the same or younger age. Using one hand with the other tucked in the pants pocket is considered rude here, done when one is expressing superiority to the other.
"Perhaps it was his all-American style but an open jacket with hand in pocket? That was way too casual. It was very regretful," said Chung Jin-suk, secretary general at the Korean National Assembly.
President Park's office has said nothing publicly about the incident and a spokesperson for Gates declined to comment.
But Internet chat rooms and social network sites are filled with views debating cultural differences and analyses of Gates' laid-back style.
"I don't know if that was ignorance or just plain disrespect," Cho Park, a Korean student studying in New York, said. "It was pretty rude of him. The thing is I'm not sure if it is rude in Western culture."
The controversy doesn't end there. Gates had met with two other previous South Korean presidents: Kim Dae-jung and Lee Myung-Bak. He apparently gave the proper handshake with both hands to the late Kim in 2002 but was spotted giving an improper shake to President Lee in 2008. That also became a subject of debate.
Some South Korean media have been speculating that perhaps it was intentional, showing his political preference; respect for the opposition leader Kim but disrespect for the ruling party leaders Lee and Park, 61.
"Cultural difference or bad manners?" the Joongang Ilbo newspaper wrote.
"A disrespectful handshake or a casual friendly handshake?" DongAh Ilbo newspaper said in its photo caption.
"It's a head of state we're talking about," said Rick Yoon, a brand retailer in Seoul. "And she's a lady. This is not just a Korean thing. It's an international protocol.
"Maybe it was intentional. Otherwise, he has a very strange habit."
Gates was in South Korea on a three-day visit to promote his start-up TerraPower, which is developing next-generation nuclear reactors.
ABC News' Joanne Kim contributed to this report.