Jones left the field with 15 minutes to play after falling heavily when defending a corner, leaving Doncaster to play the remainder of the match with ten men having made all three substitutions.
Doncaster's official website confirmed the suspected injury saying: "Rovers' Captain Rob Jones picked up a suspected broken arm in the defeat to to Reading at the Madejski Stadium.
"Rob walked off the field holding his right arm and was was taken straight to hospital.
"Speaking after the game Paul Dickov said it is too early to speculate on how long Rob will be out for."
The defeat leaves Doncaster in 17th position in the Championship.