Bangladesh are due to play three one-day internationals in Sri Lanka from July 20 to 25 at the end of the current three-test series.
Rafique, 36, is playing in the final Test which started in Kandy today and is due to return home after the match. Sri Lanka lead the series 2-0.
''The board has accepted his request for leave to attend his ailing son and he is now preparing to return home from Sri Lanka,'' BCB general secretary Mahbub Anam said.
Rafique would return to Sri Lanka only if his son completely recovered from a urinary infection, Anam said.