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Republic boss Brian Kerr has confirmed that it was the best option for the 25-year-old.
"Richard has been receiving treatment from our medical staff since his arrival this week," said Kerr.
"However following a review (tonight) our medical team felt it would be more beneficial if he returns to Manchester City for intensive treatment rather than lose a day travelling to France.
"But if he recovers sufficiently from the injury over the next few days, he will rejoin us in Dublin on Sunday," he added.
If fit and selected for next Wednesday's qualifier against the Faroe Islands, Dunne will earn his 21st cap. He last made an international start eleven months ago - in the 3-0 friendly win over Canada at Lansdowne Road.
The Dubliner has made seven Premiership appearances for City so far this season, earning rave reviews and the prospect of a new improved contract from boss Kevin Keegan in January.