Hasenhuttl, 55, replaced Mark Hughes as manager in December 2018 and oversaw 16th, 11th and two 15th-placed finishes during his time on the south coast.
Southampton currently sit 18th, a point from safety, having won only once in nine league matches.
First-team coach Ruben Selles has been placed in charge for their Carabao Cup third round tie with Sky Bet League One side Sheffield Wednesday on Wednesday.
They head to Liverpool in the Premier League on Saturday.
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