Abu Asama said: I asked Abu Abdillah (as) about the vomit, does it break the wudhu?So He (as) said: No.

Note: If one vomits while being in the state of purity, then he should rinse the mouth.
Abu Abdillah (as) said: When a man vomits while he is in the state of purity, so let him rinse his mouth.¹
¹ [al Kafi, Volume no. 3, page no. 37]