He returned to the team for the Nidahas Trophy in Sri Lanka in March after receiving treatment from Australia, where doctors had advised him to have surgery.
His pain returned during the recent Twenty20 international series against the West Indies, which Bangladesh won by 2-1 in the Caribbean and the United States.
With a busy schedule coming for Bangladesh leading up to the World Cup 2019, Shakib felt he should not delay his surgery.
"I don't want to play without being fully fit. If I think that way, it should be done before Asia Cup and that is normal," he said.
Bangladesh are drawn in Pool B with Sri Lanka and Afghanistan in the Asia Cup, scheduled to be held from September 15 to 28.