"He has been advised a week's rest, after which he will be reporting to the NCA (National Cricket Academy) for further injury management," a BCCI release said.
Delhi seamer Parwinder Awana has been selected by the All-India Selection Committee as a replacement for the injured Singh in the India A squad for the West Indies.
Awana, who represented Kings XI Punjab in IPL 5, impressed with 17 wickets in 11 games claiming his best figures of 4 for 34.
Earlier in the month, Awana failed to make it to the 15-man squad for the Caribbean tour, Awana said he used to such ups and downs in his career due to repeated ignorance by selectors.
"I have been conditioned in such a way that I have learnt to take rejections. You don't stop working hard because you have been rejected," Awana told PTI. "I have never got anything easily in my life. Even when I have played for Delhi, I treated each match as my last opportunity."
Awana, who has claimed 110 first-class wickets from 32 matches in his career, said that he expected to make the cut for the tour. "Obviously, when you get 57 wickets in the domestic season, you expect a call. I was hurt initially, but this rejection has made me more determined to perform even better in the next domestic season," he said.
India A will play three four-day matches, three one-day matches and two Twenty20s on the tour, which begins in Barbados on June 2.