Three thousand people in Uruguay and 250 people in Entre Ríos were forced from their homes on Monday amid intense rainfall and flooding. Twelve national highways in Uruguay were also cut off.
Uruguay and Argentina on Sunday suffered a historic blackout which left most of both countries without electricity for most of the day.
In Rosario del Tala in Entre Ríos province, dozens of families were evacuated on Monday and Tuesday with the assistance of provincial authorities, the Army and volunteer fire fighters.
A weather alert was in place in Buenos Aires City, including warnings of hail.
Entre Ríos Governor Gustavo Bordet told Diario Uno newspaper that evacuees were receiving assistance from the provincial government.
In Uruguay, authorities were focusing on "mitigating" the impact of "leaving one's home and seeing their belongings damaged", Presidential Secretary Juan Andrés Roballo told El País de Montevideo.
Buenos Aires City officials warned residents on Monday to avoid walking in flooded streets and leaving home amid strong winds, as well as leaving objects on balconies and terraces.
Residents are also advised against "touching cables or electricity supplies in the street", the government urged.