The principle of ahiṃsā, or “harmlessness” (or, more accurately, “nonaggression”—since sometimes “harming” may be necessary, as in breathing, which automatically kills millions of micro-organisms, or when one protects loved ones from evil aggressors), is found throughout Vedic texts and in the Vaishnava tradition in general. It traditionally refers not only to non-aggression among humans, but it is clear that it should be extended to all other living creatures as well.
The earliest reference to the idea of non-violence to animals (“pashu-ahiṃsā”) can be traced to the Kapisthala Kātha Samhita of the Yajurveda (31.11), which is said to have been written in the 8th century BCE.