The 25-year-old has undergone surgery and is expected to be out of action for several months.
Glasgow Warriors head coach Gregor Townsend said: “We’re all disappointed for Ryan that he’ll miss the final in a couple of weeks.
“Thankfully it’s not the same shoulder he injured last summer, but it’s a setback for him after he's had another very good season with us.
“We wish him all the best with his rehab.”