"Mr Ponting you must keep your mouth shut and look back to what they did against you in Cardiff last year and take a note of the latest one against Sri Lanka," Akram wrote in his column in the Daily Star newspaper here on Thursday.
"His (Ponting's) duty is to play cricket and not to think about which teams will play at this level," said Akram, who bagged 414 wickets in 104 Tests and 502 in 356 One-dayers.
Bangladesh stunned Sri Lanka by four wickets in the second One-dayer at Bogra on Wednesday, nearly eight months after their remarkable win over world champions Australia in a triangular series match at Cardiff in England.
Akram's comments came a week after Ponting told Britain's Daily Telegraph newspaper that Bangladesh and fellow-strugglers Zimbabwe should be stripped of Test status.
"What I would not have is the minnow nations in the World Cup and the Champions Trophy, and I would not have Bangladesh and Zimbabwe playing Tests at present," Ponting said in an interview.
Akram, who is here as a television commentator, said Bangladesh had the ability to beat any team in top-class cricket.
"The win (against Sri Lanka) once again gave an indication that Bangladesh can beat any team in the world if they play up to their potential," he said.
Bangladesh have lost 35 and drawn four of their 40 matches since gaining Test status in 2000. Their lone win came against a depleted Zimbabwean side at home last year.
They have won just 11 of their 117 One-dayers, beating Australia, India, Pakistan and Sri Lanka once and Zimbabwe four times. Their other wins came against non-Test-playing nations, Kenya, Scotland and Hong Kong.
Australia are scheduled to play three One-dayers and two Tests on their tour of Bangladesh in April.