Wright came off late in the 1-0 victory over Oxford United on Saturday, with Parkinson fearing that he had suffered a serious ankle problem.
Tests have confirmed that he will miss the majority of Sunderland’s run-in as they chase automatic promotion.
“It didn’t look good at the time and further tests have unfortunately confirmed that he will miss eight to 12 weeks,” Parkinson said.
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“It’s a blow for the squad, but more than anything we are disappointed for Bailey because he’s come into the team and played really well.
“I’m sure he will come back stronger, but as I have mentioned many times before, the lads currently out of the team have been excellent and we have good options available in his absence.”
Wright is out of contract in the summer at Bristol City and made a major impression in his first five appearances for the Black Cats.