Harbhajan, who was part of the T20 squad for the three-match series, was left out for the ODIs but the Punjab-born player got a lucky call-up after Ashwin could bowl only 4.4 overs at Green Park.
Ashwin's availability in the remainder of the series will be subject to medical assessment.
"R Ashwin has sustained a left side strain type injury during the first Paytm One day International against South Africa at Green Park, Kanpur on 11th October 2015. After making a detailed assessment of the injury, the BCCI medical team will confirm the time frame required for Ashwin to fully recovery from the injury," the BCCI said in a release.
India lost the T20 series 2-0, with the last game being washed off at Eden Gardens.
Ashwin stood out with 4 wickets in two T20 games amid a mediocre show by the Indian bowlers.
The Mahendra Singh Dhoni-led side, which is looking for a turnaround after being outplayed in the shortest format, will be dealt a severe blow if Ashwin sits out of the remainder of the series.
