The pandemic generated by Covid-19 caused social and economic consequences that constituted a global challenge for all countries. Italy was one of the first nations to be affected by the pandemic, especially in the heart of its production system and in the most densely populated area: the Lombardy Region. Starting in February 2020, there was a progressive slowdown until a total lockdown that paralyzed almost all social and economic activities, until a partial resumption of normal activities in May and a further increase in mid-June. The study was motivated by the fact that the electricity demand strongly decreased and changed in its typical characteristics, introducing new critical issues in the system at both the transmission and distribution levels. The goal was to analyze the strong impact of this changes on the distribution network and the transmission grid, focusing on the distribution network of Milan during the whole period. The results provide a useful example of the effects of such a pandemic and can constitute a reference valid also for many other big cities in the world.