Herath, 36, needed four stitches in the spinning finger of his left hand after he tried to stop a full-blooded drive from Jos Buttler in Wellington on Sunday.
Sri Lanka are concerned and have called up Seekkuge Prasanna as cover in case he fails to recover.
Cricket Sri Lanka tweeted: “Seekkuge Prasanna will go to Australia as a stand by for injured Rangana Herath who split his finger during the ENGvSL match #LionsRoar#lka.”
Prasanna, 29, has played 22 ODIs since his debut in 2011. He was a member of the squad which faced New Zealand in a seven-game series on the eve of the World Cup but was not selected for the showpiece tournament.
Sri Lanka won the match by with England by nine wickets and the 1996 champions are almost assured of a quarter-final spot with just two Pool A games left to play, against Australia in Sydney on Sunday and Scotland in Hobart three days later.