The 28-year-old fullback is expected to miss the rest of the Premier League season and his wages will be covered by FIFA Club Protection Programme during that period.
Ireland manager Martin O'Neill said no time scale had been put on Coleman's recovery.
"I'm not sure, I would only be guessing," O'Neill told reporters.
"Sometimes there are complications afterwards and injuries can be more prolonged, other times it can be clean and clear sailing.
"It will take some time but Seamus has great determination and sometimes those things work very much in your favour, in terms of recovery."
The Ireland skipper is also unlikely to feature in the five remaining World Cup qualifiers over the next seven months, with a possibility of an additional playoff tie in November.
"It will take some time to heal, it's a double break but it has been pinned up now and screwed in," O'Neill added.
"I know the doctors and surgeons are all very, very pleased with the way the operation has gone and now it's time for recuperation."
Ireland, who slipped to second spot in qualifying group D, next host fourth-placed Austria on June 11.
(Reporting by Hardik Vyas in Bengaluru; Editing by Gareth Jones)
