Craig sustained the injury to his left side while bowling in the second innings of the first Test yesterday. He left the field to receive treatment and did not return - but remains available to bat.
Craig took one wicket in each of the Indian innings.
The injury is expected to take four weeks to fully recover, forcing Craig to return home to start his rehabilitation programme.
Patel, also an off-spinner, (36), last played for the Test side in 2013, but has been a star performer for Warwickshire on the UK county circuit.
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Hesson said it was important to have an off-spinner in India, and that Patel fitted the bill perfectly.
"Jeetan is up to speed from a bowling load perspective having recently completed a successful county season - so he will be ready for the rigours of Test cricket," said Hesson.
The second Test between the two teams is scheduled to begin in Kolkata from Friday.
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