Gill suffered the injury on the second day of the first Test in Kolkata and spent one night in hospital, taking no further part in the match, which South Africa won by 30 runs.
Ahead of the second Test on Saturday, the Board of Control for Cricket in India said: "Shubman has been responding well to the medical treatment provided and will travel to Guwahati with the team (on Wednesday).
"He will continue to be monitored by the BCCI medical team and a decision on his participation in the 2nd Test will be taken accordingly."
Top-order batsman Gill retired hurt on four and did not return to resume his innings and nor did he field, with vice-captain Rishabh Pant leading the hosts for the remainder of the first Test.
