The 25-year-old striker is to undergo surgery on torn ankle ligaments in the United States and is expected to be out of action for four months.
Carroll has flown from New Zealand, where his team are part of the Football United Tour, for treatment after hurting his ankle during training at the start of the tour.
He had already been ruled out of matches against A-League sides Wellington Phoenix and Sydney FC because of the injury.
It is the latest setback for the big striker, who missed a large part of last season with injury after joining West Ham from Liverpool for £15 million in June last year.
"He was really looking forward to getting up and running this season and he's had a bit of a set-back. It's disappointing for him," Downing said ahead of their clash with Sydney in Wellington.
"It's a big blow for the team. He's a big player for us. But it's a chance for someone else to come in and stake their claim.
"It's disappointing for Andy. But it's a long season and we'll get him back as quick as we can."
West Ham will be hoping to bounce back from their disappointing 2-1 loss to the Phoenix on Wednesday.
Sydney were outclassed 4-0 by Newcastle United in the opening match of the four-team tournament in Dunedin on Tuesday but Downing felt not too much could be read into either result.
"Everyone was expecting us to turn up the other day and win that game and we lost. So you can never take these games lightly," he said.
"The big thing for us is that we're due a big performance because we weren't really that good the other day."
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