Leach sustained the injury during the first Test in Hyderabad, leading to his exclusion from the second match.
The left-arm spinner will travel back home from Abu Dhabi, where England are currently stationed during the long gap between the second and third Test, which begins on Thursday in Rajkot.
"Leach will work closely with the England and Somerset medical teams in respect of his rehabilitation," ECB said in a statement on Sunday.
Currently, England have not named a replacement for Leach. However, the squad boasts a formidable spin contingent, including Rehan Ahmed, Tom Hartley, and Shoaib Bashir, complemented by the part-time option of Joe Root.
