Lee, 33, will be sent home after suffering the strain in Australia's shock defeat to Zimbabwe, adding to a long line of injury woes. Team officials have asked for permission to call up a replacement.
"It's a muscle strain on the inner side of the elbow of the right arm," a Cricket Australia spokesman told AFP, adding that it was separate to the elbow problem which recently required surgery.
"It was scanned but it will need to be looked at tomorrow," he said.
Lee, who has also battled foot, ankle and rib problems, retired from Test cricket in February to prolong his career in the shorter forms of the game.
Reports said Doug Bollinger or Ryan Harris were likely to be called up if the International Cricket Council (ICC) gives Australia permission to replace Lee.
Australia suffered a shock, one-run loss to minnows Zimbabwe in the warm-up game in St. Lucia, ahead of the 12-team World Twenty20 which starts on Friday.
Copyright AFP (Agence France-Presse), 2010