Abreu is the third Dodgers third basemen to get hurt, following Andy LaRoche and Nomar Garciaparra, who both sustained injuries March 7 against the Cardinals at Holman Stadium. LaRoche suffered a tear of the ulnar collateral ligament in his right thumb and Garciaparra was hit on his right wrist by a pitch.
Abreu was hitting .208 in 24 at-bats, as he was trying to overcome the effects of hernia surgery last October.
With Garciaparra, LaRoche and now Abreu out for the start of the season, the Dodgers are down to Blake DeWitt and Chin-Lung Hu.
"He was a non-roster invite and he's still here," Torre said of DeWitt. "He's played well and everyone around him is falling down."
Because of the injuries to the infield, Torre said the club is thinking of keeping 14 players and only 11 pitchers to start.
One pitcher who won't be making the Opening Day roster is Mike Myers, who was released Thursday.
"It's a shame, because I thought he was pitching well," said Torre, who said he felt bad, but it was just a matter of numbers.
In 7 2/3 innings, Myers had given up 10 hits and struck out four, while allowing seven earned runs to score.
Glenn Rabney is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.