Sports minister Dayasiri Jayasekera said he ordered an inquiry after Malinga lambasted him for questioning the endurance of Sri Lankan players following their failure to reach the Champions Trophy semi-finals.
"He is now under investigation for making statements to the media in breach of his contract with Sri Lanka Cricket (board)," Jayasekera told AFP.
"In my criticism of the appalling fitness levels of our players, I did not name Malinga, but he has chosen to put the hat on and attack me publicly."
"I don't care about criticism from those who are simply warming chairs," he said. "What does a monkey know about a parrot's nesting hollow? This is like a monkey getting into a parrot's nest and talking about it."
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Jayasekera said some Sri Lankan players had pot bellies that stopped them moving and that often they could not hold catches.
Pakistan skipper Sarfraz Ahmed was twice dropped in his side's Champions Trophy win over Sri Lanka. Both catches were off the bowling of Malinga, who ended up with just one wicket for 52 runs.
"The typical body fat amounts for a cricketer should be about 16 percent, but most of our players have over 25 percent," Jayasekera said.
"I want the results analysed and in future no one will be included in a national squad if they are above 16 percent."
Malinga, 33, was a surprise choice for the Sri Lanka squad as he has played little international cricket in the previous 18 months because of injury.
Malinga was the only player excused from Sri Lanka's high altitude training camp before the Champions Trophy, because of the IPL campaign.
"They improve their fitness level just to bowl four overs at the IPL," Jayasekera said, referring to Malinga. "These guys are not interested in playing for the country, they play for the IPL because of the money they get."
Jayasekera said he was also making fitness a key requirement for other sports before an athlete can participate in overseas tournaments.