Craig claimed two wickets in the first test in Kanpur but left the field after sustaining an injury to his left side while bowling in the second innings.
"We're really disappointed for Mark, knowing the work he’s put in to prepare for this series," coach Mike Hesson said in a statement.
The 29-year-old will fly home for rehabilitation and is likely to take four weeks to fully recover.
In a like-for-like replacement, 36-year-old Patel returns to the squad having played his last test against South Africa in 2013.
"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," Hesson said.
"He'll also add invaluable experience to our young spin group."
Patel is the second spinner of Indian-origin in a touring party that also includes leg-spinner Ish Sodhi.
Kolkata hosts the second of the three tests from Friday.
(Reporting by Amlan Chakraborty in Kanpur; editing by Nick Mulvenney)
