Does wither apply -1/-1 counters even if the creature receiving damage has indestructible?

Wither is a static ability that changes the way a source deals damage to creatures: instead of marking damage on the creature, it places an equal number of -1/-1 counters on it (CR 702.79a). This replacement effect happens at the moment damage is dealt and has nothing to do with how the game later checks whether a creature should be destroyed.

Indestructible means a permanent cannot be destroyed by damage or by effects that say 'destroy' (CR 702.12b). It does not prevent -1/-1 counters from being placed on a creature. Those counters reduce the creature's toughness, and if toughness is reduced to 0 or less, the creature is put into the graveyard as a state-based action — not because it was 'destroyed' (CR 704.5f). So even an indestructible creature can be killed this way.

Concretely: you attack with a 3/3 creature with wither. Your opponent blocks with an indestructible 4/4. The 3/3 deals 3 damage, which wither converts into three -1/-1 counters. The 4/4 is now effectively a 1/1 (still indestructible). If anything later adds two more -1/-1 counters, its toughness hits 0 and it goes to the graveyard via state-based action — not destruction.

In summary, wither and indestructible interact in a nuanced but clear way: wither bypasses the damage-marking step entirely, placing counters instead, and indestructible offers no protection against that counter placement or its consequences.