Shoriful picked up the injury after taking 4-44 in the third ODI against Zimbabwe, forcing him to leave the tour immediately after the match.
The 25-year-old returned home and began rehabilitation after a week of rest. The BCB later confirmed that he had suffered a Grade 1 hamstring injury, making his participation in the first Test doubtful.
Shoriful has now reportedly passed his fitness test and is expected to link up with the team before the second Test in Mackay, starting August 22. His return would provide a timely boost to Bangladesh's pace attack.
Bangladesh, however, remain without another key fast bowler, Nahid Rana, for the entire Australia tour. Nahid is recovering from a Grade 2 side strain, leaving Bangladesh with limited options in the pace department.