(1) Background: During the COVID-19 outbreak, several studies showed an increased prevalence of extended-spectrum β-lactamase producing Enterobacterales (ESBL-PE) carriage in intensive care units (ICUs). Our objective was to assess the impact of antibiotic prescriptions on the acquisition of ESBL-PE in ICUs during the COVID-19 crisis. (2) Methods: We conducted an observational study between 1 April 2020, and 31 December 2021, in the medical-surgical ICU of the Cayenne General Hospital. We defined two periods: Period 1 with routine, empirical antibiotic use, and Period 2 with no systematic empiric antibiotic prescription. (3) Results: ICU-acquired ESBL-PE carriage was 22.8% during Period 1 and 9.4% during Period 2 (p = 0.005). The main isolated ESBL-PE was Klebsiella pneumoniae (84.6% in Period 1 and 58.3% in Period 2). When using a generalized linear model with a Poisson family, exposure to cefotaxime was the only factor independently associated with ESBL-PE acquisition in ICU (p = 0.002, IRR 2.59 (95% IC 1.42–4.75)). The propensity scores matching estimated the increased risk for cefotaxime use to acquire ESBL-PE carriage at 0.096 (95% CI = 0.02–0.17), p = 0.01. (4) Conclusions: Exposure to cefotaxime in patients with severe COVID-19 is strongly associated with the emergence of ESBL-PE in the context of maximal infection control measures.