Boucher left the field on Monday towards the latter part of the Indian first innings and Abraham de Villiers did the duty with the gloves.
However, scans taken later in a local clinic indicated that it's only a strain and he should be available for the second Test starting in Kolkata on February 14, Cricket South Africa's media officer Michael Owen-Smith said.
"CT scan and MRI scan have given him a clean bill of health. It's a lower back sprain and he will continue ongoing treatment from the physio," Owen-Smith said.
"I'm not putting a time frame when he will be back on field but we are confident he will be ready for the Kolkata Test afterwards," he added.