Fast bowler Wayne Parnell also suffered a pinched nerve during a SuperSport Series match but he has been cleared for the ODIs. The series begins in Paarl on January 11.
Elgar suffered a knee injury while playing for the Knights against the Cape Cobras during the SuperSport Series matches over the weekend. "It is feared that he may have suffered ligament injury, which could necessitate surgery," Cricket South Africa said in a media release.
Morkel has not played for South Africa since November 2010. He suffered an abdominal muscle tear while playing for Chennai Super Kings in the Champions League T20 and then had surgery at the beginning of the South African summer.
Morkel, however, has been in good form for the Titans, scoring 127 not out and 55 not out, and taking wickets in the ongoing SuperSport Series match against Warriors. He will join the South Africa squad on January 9.