The 32-year-old took four wickets in the first two ODIs but was injured in his second over of the third match.
His unavailability is a blow for the tourists, who have taken an unassailable 3-0 in the series ahead of the fourth ODI in Adelaide on Friday.
"It was really unfortunate, Liam is going to be out for around 10 days," Morgan said. "He's going to stay with the squad for his rehabilitation.
"He's been a huge part of our progression over the past two years. We're looking at the T20 series for when he will come back so there will definitely be a change for tomorrow."
The final match of the series will be played in Perth on Sunday before England, Australia and New Zealand square off in a tri-nation T20 series that begins on Feb. 3.
England open their T20 campaign against Australia on Feb. 7.
First Published: January 25, 2018, 7:10 PM IST