The left-handed opener had been struggling with a meniscus problem and travelled to Australia after Christmas to consult with orthopaedic surgeon Dr David Young.
An update from the Bangladesh Cricket Board said he would start rehab as soon as possible and should be back practicing with the team in less than three weeks.
They open their World Cup Pool A campaign against Afghanistan on February 18 in Canberra.
A statement read: “Tamim Iqbal underwent an arthroscopic evaluation and surgery for a left meniscal pathology at the Avenue Hospital in Melbourne today. The procedure was performed by orthopedic surgeon Dr.David Young.
“BCB???s senior physician Dr.Debashish Chowdhury, who has been in constant contact with the surgeon, informed that Dr.Young is confident that Tamim will be able to return to cricket practice in two-to-three weeks following his rehab which will begin immediately.
“The BCB medical team will decide on the management plan for the player in consultation with Dr. Young after evaluating the complete report on the surgery.”