One should distinguish between the notational zero (i.e., as placeholder in a positional system for representing numbers) and the algebraic zero (i.e., as the neutral element of addition). We use the same symbol for both (and with good reason), but they were introduced independently.
As far as I know, the first mention of the algebraic zero is in the Brāhmasphuṭasiddhānta (ca. CE 628) of the Indian mathematician Brahmagupta, specifically in the section Kuttaka ("pulverizer"), Rule §19. Quoting from Thomas Colebrooke's translation of 1817 (Section II, 31 on page 339):
[...] The sum of two affirmative quantities is affirmative; of two negative
is negative; of an affirmative and a negative is their difference; or, if they be equal, nought. The sum of cipher and negative is negative; of affirmative and nought is positive; of two ciphers is cipher.
(Brahmagupta uses the two terms nought (Sanskrit खम्, /kham/) and cipher (Sanskrit शून्यम्, /śūnyam/) indiscriminately.)
For those interested, the two sentences in transliteration read
dhanayos dhanam ṛṇam ṛṇayos dhana-ṛṇayos antaram sama-aikyam #kham/
ṛṇam aikyam ca dhanam ṛṇa-dhana-#śūnyayos #śūnyayos #śūnyam//