Stetina broke his right tibia, patella and four ribs in the crash which came just 400 metres from the finish of the 162.7km stage in Bilbao.
The crash occurred as the peloton passed a set of meter-high metal poles topped with orange traffic cones near the curb lane of the finishing straight.
Stetina is set for a long rehabilition and will miss several of his season goals, including the Amgen Tour of California.
"The Amgen Tour of California was my big goal and my GC (general classification) race this year," Stetina said. "Now it is almost for sure out the window."
Yates's injuries were less serious but the result will be the same for him as he continues his progression in the professional ranks.
A break to his right middle finger was confirmed after he was taken to hospital for scans.
The crash comes shortly after two riders were knocked off their bikes by neutral support vehicles at last weekend's Tour of Flanders and will no doubt hasten calls for a full review of safety procedures in professional cycling.