The former Italy and Chelsea No 2 took over from Steve Clarke in the summer but has been relieved of his duties with Killie sitting fifth in the table.
Alessio was voted Ladbrokes Premiership Manager of the Month in October but Kilmarnock have won just one of their last eight matches.
Assistant Alex Dyer has been put in interim charge of first-team duties, with the club's next match against Motherwell on Saturday.
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