While Stokes, who was born in Christchurch, had said the trip was to visit family, it fuelled speculation the 26-year-old was preparing for a recall to the Ashes squad.
However, with England handing back the urn after three straight defeats, Saturday's announcement virtually rules him out of taking part in the remainder of the test series.
Canterbury CEO Jez Curwin said Stokes had made a good impression at the club.
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"We can't fault his attitude or his all-round contribution in his time with us and we are sorry that he couldn't stay with us for longer but Ben knows that he will always find a welcome here should the opportunity arise for him to return," Curwin said in a statement on the team's website.
Stokes said he had "thoroughly enjoyed training and playing with Canterbury".
"It's a wonderful club and I couldn't have asked for any more from my time here," he said in the statement.
The Ashes series continues with the fourth test in Melbourne, starting on Dec. 26, and finishes with the fifth test in Sydney from Jan. 4-8.
While Stokes now looks certain to miss the remainder of the test series, he has been provisionally named in England's squad for the five-match ODI series against Australia which follows the Ashes.
(Writing by Peter Rutherford, Editing by Sudipto Ganguly)
