The injury, sustained when he was playing for Ireland in their Euro 2016 qualifier against Poland on Sunday, means he is doubtful for Ireland's Euro 2016 play-offs next month.
Koeman said the striker, who scored with a spectacular shot when Ireland beat world champions Germany 1-0 last week, is facing two to four weeks on the sidelines.
Speaking to reporters before Southampton face Leicester City on Saturday, he added: "The Shane injury is a disappointment. It's an ankle ligament injury and he will be out for two to four weeks."
With the Dutch failing to qualify for the Euros after a 3-2 home defeat by the Czech Republic on Tuesday, Koeman could be the man to revitalise the side if current boss Danny Blind is sacked or quits.
But he appeared to dash any Dutch hopes of an immediate return when he was asked about his future.
"I am the manager of Southampton and I'd like to stay. After this year I have one more season left on my contract so there is no possibility," he said.
"One day maybe in the future -- but it depends on a lot of things and about what happens in Holland."
He also implied he did not think the Dutch were going to get back to the heights they have touched over the last 40 years, like reaching the World Cup final in 2010 and finishing third in Brazil last year.
"The competition in Holland is not the best one, it is a good school for young boys but they are still not ready for the highest level. It is difficult and we have to change but it is not up to me," he said.
(Reporting by Mike Collett; editing by Martyn Herman)
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