The warning is in place for the 24 hours between 9pm on Tuesday and 9pm on Wednesday. It covers all of Connacht and Munster, as well as Co Kilkenny.
Rainfall accumulations of between 30mm and 50mm are expected during that period. In Cork and Kerry, higher accumulations are possible in hilly and mountainous areas.
Met Éireann has also warned of the risk of spot flooding on Wednesday. Successive bands of heavy rain are forecast to alternate with brighter periods for the rest of the week.
Additional costs associated with poor weather conditions led to European Commissioner for Agriculture and Rural Development Phil Hogan deciding to allow a 70% BPS advance next month, he said during a visit to Ireland last week.