Team officials remain confident Clarke will be able to play in the match, starting at Headingley on Friday, but have instructed him to skip Wednesday's training session as a precaution.
"Michael Clarke has an abdominal strain that became sore after the completion of (Monday's) game," Australian physiotherapist Alex Kountouris said in a statement.
"He will continue to be treated with a view to him being fit for the fourth test beginning on Friday."
Clarke has been the leading batsman of the series, scoring 352 runs at an average of 88 with centuries in each of the past two tests.
England lead the five-match series 1-0 after winning at Lord's while the rain-interrupted matches at Cardiff and Edgbaston were drawn.