Does wither apply to creatures that have indestructible?

Wither is a damage-replacement effect (CR 702.79a): instead of marking damage on a creature in the normal way, it causes that damage to be dealt as -1/-1 counters placed on the creature. This happens regardless of whether the damaged creature has indestructible.

Indestructible (CR 702.12b) only prevents a permanent from being destroyed — either by the 'destroy' keyword or by state-based actions that would destroy a creature due to lethal damage. Because wither never marks 'damage' at all, the indestructible clause about lethal damage never even comes up.

However, the -1/-1 counters themselves reduce the creature's toughness. State-based actions (CR 704.5f) check whether a creature's toughness has been reduced to 0 or less, and if so, the creature is put into the graveyard — this is NOT destruction, so indestructible does NOT save it.

Example: You attack with a 3/3 creature with wither. Your opponent blocks with a 4/4 Angel that has indestructible. Your creature deals 3 damage, placing three -1/-1 counters on the Angel, making it a 1/1. It survives this combat. But if the Angel had been a 3/3, all three counters would reduce its toughness to 0, and state-based actions would put it into the graveyard despite its indestructible ability.

So wither is one of the few ways to effectively handle indestructible creatures in combat — keep piling on -1/-1 counters until toughness hits 0.