Photos released by the US-based Simon Wiesenthal Centre appear to show red banners with swastikas as well as smiling students wearing Nazi uniforms or saluting, some with swastikas painted on their faces.
A government official said on Wednesday that, according to the Sacred Heart College in the northern city of Chiang Mai, the parade was organised by the students, who had not intended to cause offence.
"The school officially explained that it was an internal sports day and students who were in the red team wanted to give a surprise by using swastikas as the background since it's the colour red," said Charnwit Tupsuphan, secretary of the Private Education Commission, a government body.
"Both students and the school expressed their regret and apologised," he added. "I've instructed all schools to be more careful about this kind of issue and to use it as a lesson."
The Israeli embassy said it had received a letter of apology after contacting the school.
"I think that really it was done out of ignorance, not out of bad intentions," Itzhak Shoham, the Israeli ambassador to Thailand, told AFP.
"Many people here in Asia are not aware of what happened in Europe," he added. "They tend to think that he [Hitler] was a hero and not a monster as he really was so I think it is important to strengthen the educational level."
In a statement on its website, the Simon Wiesenthal Centre called for "immediate action against all those responsible for promoting and facilitating this disgraceful display", noting that a similar incident had taken place at another school in Bangkok in 2007.
"It is difficult to calculate the hurt such a display inflicted on survivors of the Nazi Holocaust and the families of all victims of Nazism," it said.
The school could not immediately be reached for comment.