The ultimatum came after the squad was found to be unfit for the series against Zimbabwe which starts Friday.
"No one has a satisfactory level of fitness, but I have made an exception this time," sports minister Dayasiri Jayasekera said.
Players are selected by an independent panel for the national team, but the sports minister must give final approval before they can represent the country.
Jayasekera said no member of the 13-man squad met required international fitness standards and noted that high levels of injuries were due to poor endurance.
Controversial fast bowler Lasith Malinga who weighs 80 kilos (176 pounds) failed one test, the source said, and barely scraped through the rest. He is officially under observation.
"Malinga has suffered recurring injuries partly because of the poor fitness," the source said on condition of anonymity.
Malinga was slapped with a fine of 50 per cent of his match fee for Friday's game and given a six-month suspended match-ban for comparing Jayasekera to a "monkey" and saying the minister knew nothing about cricket.
The typical body fat amount for a cricketer was 16 percent, but most Sri Lankan players had over 26 percent, Jayasekera said.
He has warned any player with a body fat percentage over 16 will not be allowed to represent the country.
Sri Lanka Cricket announced Tuesday that Malinga had apologised and also pleaded guilty to violating his contract with the board which precludes players from making public statements.
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