Vietnam coach Park Hang-seo told Thailand assistant Sasa Todic he was ready to fight him following an apparent insult about his height following a World Cup qualifier.
The touchline row was sparked at the end of Tuesday's draw between Vietnam and Thailand in Hanoi. Park shook hands with his opposite number Akira Nishino at full-time in front of 40,000 fans.
Meanwhile, Todic, a former goalkeeper from Serbia, was grinning and made a gesture with his hand level with his chest, leading to the South Korean having to be restrained.
"During the course of the game, I saw that he occasionally smiled at me," Park, 60, told reporters. "If he wants to fight, I'm ready."
Vietnam Football Federation vice president Tran Quoc Than confirmed that an official complaint had been made to the Asian Football Confederation.
Sources have told ESPN FC that senior Thai FA officials made it clear to Todic on Thursday that his actions were unacceptable.
Todic later apologised, claiming that his gesture has been misunderstood.
"All that is published in the media and on social networks has nothing to do with reality, especially not with RACISM as some media conveyed," Todic said in a statement released by the Football Association of Thailand, explaining that the movement of his hand was in reference to Vietnam's lead at the top of Group G being temporary.
Todic added: "The finger was pointed only at me as there is a photo of what it looks like I am measuring the height of the coach. This is the moment that the media use to make a scandal, although there is a footage that can deny it because it can be seen that I have shown a top-down hand thinking that Vietnam is currently in first place, but that it will fall lower later because Thailand will be ahead of them.
"I take the opportunity to apologise to anyone who misinterpreted my reaction. Judging by the comments, a large number of Vietnam fans were offended by untrue media reports, seeing only the picture and not knowing the true truth."