Maro Itoje has broken his right hand and is a major doubt for England's autumn internationals.
The big showdown at Twickenham on November 12 has already been spiced up by England coach Jones' comment that the Boks are "bullies", but now he won't have one of his own enforcers available for games against South Africa, Fiji, Argentina and Australia.
"Maro came off with a sore hand", said the Saracens director of rugby, Mark McCall.
"George is on the road to recovery and we look forward to his return to action sooner rather than later".
The England worldwide was replaced in the 46th minute of Saturday's 44-26 Champions Cup win over Scarlets and has been ruled out for six weeks.
Itoje went off early in the second half of Saracens' 44-26 win over the Scarlets after his arm was trapped awkwardly as he made a tackle.
Hartley will line up for Saints in their European Champions Cup clash against Castres, having been sidelined since mid-September due to back trouble.
Kruis was a key member of the England side that won this year's Six Nations Grand Slam and the summer Test series in Australia.
In 2016 he led Saracens to the European Champions Cup final against Racing Metro 92 which they won 21-9 with Itoje picking up the man of the match award.
Itoje had been touted to move from lock, where England are well served with replacements, to the problem area of flanker following the injuries to James Haskell, Jack Clifford, Mike Williams and Sam Jones.
He could now revert to a second row combination of Courtney Lawes and Joe Launchbury.
But it looks as if Jones will now have to select a specialist back-row in that position.