It would appear there is no Greek small caps built into Minion Pro.
You can achieve what you want using GREP Styles if there is a way to target lowercase Greek letters. I don’t think there is a wildcard specific to lowercase Greek letters so you would have to use or (vertical bar) between each letter you want to find. Then apply a small caps character style. I find the best way to make that is to use horizontal and vertical scaling then increase the font weight a bit (normal to semibold, for example).
Here I have made a small caps character style that uses Minion Pro Caption, vertical scaling is 67%, horizontal scaling is 70%. I then used a GREP Style to apply it to lowercase Greek letters with this term:
(α|β|γ|δ|ε|ζ|η|θ|ι|κ|λ|μ|ν|ξ|ο|π|ρ|ς|σ|τ|υ|φ|χ|ψ|ω|\l)
