From Zelda Wiki.org
Chasers appear in both
The Minish Cap and
Oracle of Seasons. In either case, they are similar to
Blade Traps in that they will chase Link if he crosses their path in one of the four cardinal directions. They move slower than Blade Traps however, and will not return to their original position once reaching a wall. They will instead stop at their new position, and "chase" Link from there. As to be expected, Chasers are often found in narrow corridors where they are harder to dodge.
Quote from
The Legend of Zelda: The Minish Cap Chaser figurine:
"Appears in dungeons. They move quickly to chase you once they spot you. Your shield will block them, but keep on your toes!"