The club announced on Monday that he had flown home “due to a family emergency”, adding that they hoped he would be able to return to the UK in due course.
Steve Snell, performance director at Gloucestershire, said: “We thoroughly support Naseem’s decision to return home to see his father. Of course we will miss him on the field, but Naseem’s wellbeing and the health of his loved ones far outweigh any cricketing priorities.
“We have loved having Naseem with us as part of the Gloucestershire family and we are looking forward to welcoming him back to us as soon as possible.
“Everyone at Gloucestershire cricket is thinking of Naseem and his family and sending our upmost support”.
Gloucestershire are currently mid-table in the South Group of the Blast, with two wins and two defeats, as well as a no-result. Their next fixture is against Glamorgan at Cardiff on Tuesday, before back-to-back matches against Somerset and Sussex on Thursday and Friday.
Shah has also been signed by Welsh Fire to play in the Hundred, which begins in August.