After an hour of the team's second workout in Japan, Mellberg came in hard and late on Ljungberg.
Ljungberg reacted angrily, grabbing his compatriot, before Daniel Andersson and Henrik Larsson stepped in to separate the pair.
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Both players later played down the incident.
"Such things happen when you play," said Arsenal midfielder Ljungberg.
"If one [player] has been making tackles like that you have to respond.
"It happened a few times that he was a bit late tackling me. You can't tolerate that, but it's forgotten now," he concluded.
Aston Villa player Mellberg also said that the incident was in the past.
"Of course I regret it. You can't put a positive spin on what I did," he said.
"It is nothing you can be proud about. It was stupid."
Ljungberg is seen as crucial to Sweden's hopes after his amazing run of form at the end of the season helped Arsenal to a domestic Double.
He missed the recent friendly against Paraguay after his club exertions, but he is expected to line up in the maych against Japan on Saturday.