How mini are you talking here?
If it's on the order of stellar mass (even 1 solar mass), its event horizon will be small, but its gravitational effects even well beyond the horizon will not. It's going to rip the star apart in short order, with fantastic fireworks along the way. If it's much smaller in mass than the star, then there are other problems. The first of which is that, absent forming that black hole in close proximity to the star (in which case, why isn't it just orbiting harmlessly?), it's going to basically fall at the star at around escape velocity. It's going to be so much denser than the star (and the smaller it is, the denser it is, using the event horizon as its size) that I would expect it to basically just punch a hole through the star and keep on flying out the other side, never to return.