Can an Arduino detect a current drop
To detect a magnet it is useful to start by using a magnetic field detector. "detecting the current drop" is a step off the main path - unless you are actually trying to detect a current drop - if so, you should say so. 

A Hall sensor does just what you want - and is available off the shelf at good 

prices and with well defined characteristics -  why would you not start there?

A GMR (giant magneto resistive effect) sensor measures change in magnetic alignment - also off the shelf. (vaguely closer to what you want) 

A MEMS gyroscope and accelerometer package often incorporates a 3 axis magnetic field detector as a bonus, What's not to like?

A fluxgate sensor will probably do what you want.

Even a  mechanical deflecting sensor (compass needle like) can be bought or built from scratch.

All have the advantage of availability and or working in a known way. 

But and :-) - you can but magneto resistive sensors off the shelf -  eg here - from Arrow