Python 2, 60 bytes

c=lambda f,n,l=[]:lambda a:n-1and c(f,n-1,l+[a])or f(*l+[a]) 

Try it online!

The footer is a tester which uses STDIN in the following way per line:

1. The function itself
2. The number of the function's arguments, ≥2
3. A list of the arguments ([a,b,...])

Note that, while a list of the arguments is given as input in the tester, in reality, the curried equivalent gets prepended to the list and the list is reduced by function call.