MIDI is serial, but it's a current loop rather than a voltage level interface like the serial port. I'm thinking one of the MIDI interfaces made for the Amiga should work, assuming the MINIMIG serial port has the power voltages for the interface. (And they're on the right pins.)
That said, I remember running a cheap Casio keyboard on my Amiga with an interface made from one resistor and a DIN plug. It's the MIDI in that needs optical isolation. Unfortunately I don't remember the specifics... maybe it was on Aminet
