Anderson suffered his injury, which has been diagnosed as a grade one tear, in the first innings of the remarkable Test match at Cardiff.
He did not bowl in Sri Lanka's dramatic second-innings collapse, which left them all out for 82 in 24.4 overs on the final afternoon, as England captured victory when a match badly affected by rain seemed certain to be drawn.
“The coaches have been impressed with him and we just wanted another option, with James Anderson stepping out, other than the tall bowler in Steven Finn”
Given Sri Lanka's fallibility to the rising delivery England may decide to include 22-year-old Finn, who took 14 wickets in three Ashes Tests last winter, in a three-man pace attack of tall bowlers with Stuart Broad and Chris Tremlett.
England are hopeful that Anderson will recover for the third and final Test of the series, which begins at the Rose Bowl, Hampshire, on 16 June.
National selector Geoff Miller said: "It's obviously disappointing to lose Jimmy Anderson for the next Test as he is world-class and the leader of our attack but we're fortunate to have a healthy stock of pace bowlers at present.
"We're hopeful Jimmy will be available for the third Test but in the meantime we're excited by Jade Dernbach's inclusion.
"Jade is a talented young bowler and after excelling with the England Performance Programme over the winter he enjoyed considerable success with the ball against Sri Lanka while playing for the Lions."
England coach Andy Flower added: "The coaches have been impressed with him and we just wanted another option, with James Anderson stepping out, other than the tall bowler in Steven Finn.
"We'll monitor the conditions at Lord's and pick what we think is the best line-up.
JONATHAN AGNEW COLUMN
“Sri Lanka must be honest and admit that this was a disaster”
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