The 25-year-old has undergone surgery and is expected to be out of action for several months.
Wilson has played 79 times for Glasgow and has nine Scotland caps.
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."
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland