Visceral adiposity is a risk factor for severe COVID-19 and a link between adipose tissue infection and disease progression has been proposed. Here we demonstrate that SARS-CoV-2 undergoes productive infection in adipocytes, although the degree of infection and the cellular response depend on the anatomical origin of the adipocyte and the viral strain. Differentiated adipocytes from human visceral adipose tissue are more permissive to SARS-CoV-2 infection than their subcutaneous counterpart, and this associates with ACE2 expression. Infection of subcutaneous adipocytes leads to inhibition of lipolysis, while infection of visceral adipocytes results in higher expression of pro-inflammatory cytokines. Infected adipocytes begin to die 4 days after infection, regardless of the origin. The viral load and cellular response are attenuated when adipocytes are infected with the SARS-CoV-2 variant P.1. Hence, SARS-CoV-2 infects and replicates in adipocytes, where it compromises cell viability and alters lipid metabolism or elicits a pro-inflammatory response depending on the fat depot and the viral strain.