For an act to be suicide in the meaningful sense, the animal would need to understand that (1) death exists as a concept, (2) death is permanent, (3) their specific action will cause their own death, and (4) they are choosing that outcome intentionally. That's a substantial cognitive stack.

Animals that get closest:

Great apes, cetaceans (dolphins, whales), and elephants demonstrate some building blocks. Elephants exhibit prolonged mourning behaviors and return to bones of deceased relatives. Chimpanzees show what appears to be grief and depression after deaths of companions. Dolphins can voluntarily control their breathing (unlike humans), which has led to claims—most famously by Ric O'Barry regarding the dolphin Kathy who played Flipper—that captive dolphins have "chosen" to stop breathing.

Why scientists remain skeptical:

Most researchers interpret these cases as stress-induced physiological collapse, severe depression leading to refusal to eat, or maladaptive responses to captivity rather than intentional self-termination. The distinction matters: a grieving animal that stops eating and dies isn't necessarily choosing death—it may simply lack the will to continue life-sustaining behaviors, which is phenomenologically different from understanding that inaction leads to permanent cessation of existence.

The philosophical wrinkle:

We can't access animal subjective experience directly, so distinguishing "gave up" from "chose to die" may be empirically impossible. Some argue this makes the question unanswerable rather than answerable in the negative.

(http://www.autoadmit.com/thread.php?thread_id=5818411&forum_id=2).#49569311)