The former Queensland Red who was making his first competitive start for the province after signing in the summer, is added to a growing back row injury list which has already seen captain John Muldoon, Johnny O'Connor and Andrew Browne sidelined.
"It's not looking good for Ezra. We are waiting for the results of the scan but, even being optimistic, it looks like he will be out for at least four to six weeks," Elwood told the Irish Times.
"We have made a couple of enquiries, but nothing has come out of those yet.
"Last week we had a problem in the front row, and now we have a dilemma in the back row. Andrew Browne is not yet up to speed with his injury and it is not something we want to rush, so we are looking at a temporary replacement to get us out of a hole."
Connacht travel to Wales this weekend to face the Scarlets in search of their first league victory away from the Sportsground since April 2008.