Narine, 35, announced his retirement from international cricket in 2023, four years after playing his last match for West Indies against India
The opener left the field retired hurt after pulling a muscle in the fifth over against South African Invitational XI at Willowmoore Park in Benoni on Thursday morning.
Tamim played just 13 balls, opening the match with a boundary.
The vice-captain will be sent to a hospital for a scan to know the status of his injury.
Bangladesh will start the two-Test series against South Africa at Potchefstroom on Sept 28. This will be a key overseas test for the Tigers after brilliant performances at home in past few years.
This will be the first Test in South Africa for Bangladesh after 2008.