The 28-year-old has a left side strain which he suffered in England's opening Champions Trophy match with Bangladesh last Thursday.
He told Press Association Sport with the recovery time generally four to six weeks he was 'up against it' in being fit for the first of the four Test series.
"It's a left side strain and there is a tear in the muscle," he said.
"It's a grade-two injury, which is not terrible news, but it's not great news at the same time.
"I'm on day five of recovery now, and the physios say for the first 10 to 14 days there's not a lot we can do other than rest it.
"You don't rule it out, but I'm probably up against it for the first Test. Sometimes these things heal quicker, sometimes they take longer, so we have to play it by ear."
Woakes, who has played 17 Tests and 63 One Day Internationals, said he wouldn't risk returning too early just so he could play in the Test.
"The timing of it is frustrating, it's terrible, but it's one of those things.
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