He will be assessed by a consultant to determine the length of his recovery.
Billy Vunipola broke his right arm twice last season, once against Ospreys in the Champions Cup in January and again during England's second Test defeat to South Africa in Bloemfontein five months later.
The 25 year-old had endured a torrid 2017 before that, missing the 2017 British and Irish Lions tour to New Zealand to undergo shoulder surgery and then suffering a knee injury that required another operation upon his return.
With Nathan Hughes suspended and facing a disciplinary hearing this week and Sam Simmonds out until 2019 with a knee ligament injury, Jones faces a back-row re-think.
Two possible options to wear the No 8 shirt in November are Bath's Zach Mercer, who was involved in last month's training camp, and Ben Morgan of Gloucester.
Morgan won the last of his 31 caps in England's tournament-ending defeat to Australia at Rugby World Cup 2015.
England's walking wounded | Players unavailable to Eddie Jones
PROP
Mako Vunipola (calf)
Ellis Genge (knee)
Beno Obano (knee)
Matt Mullan (knee)
LOCK
Joe Launchbury (knee)
Jonny Hill (hand)
Nick Isiekwe (ankle)
BACK ROW
Billy Vunipola (arm)
Sam Simmonds (ACL)
Nathan Hughes (expected ban)
Jack Willis (knee)
SCRUM-HALF
Dan Robson (ankle)
CENTRE
Jonathan Joseph (ankle)
Ben Te'o (thigh)
WING
Anthony Watson (Achilles)
Marland Yarde (knee)
... and ...
Joe Marler (prop, retired)