Carroll, who is on loan from Tottenham, was hurt during England Under-21s' 1-0 victory over the Czech Republic last Friday.
He scored the only goal as England triumphed in Prague.
A Swansea spokesman has confirmed that the 22-year-old midfielder is now expected to be out for between four and six weeks.
Carroll has so far made 18 appearances for the Swans after joining them last summer on a season-long loan.
Swansea manager Garry Monk, meanwhile, is understood to be awaiting results of a scan on winger Jefferson Montero, who reportedly suffered a muscle strain playing for Ecuador against Mexico last weekend
Swansea resume their Barclays Premier League on campaign on Saturday when they host Hull City.
Source : PA
Source: PA