Background: The aim of our study was to analyze the factors associated with the increased risk of urinary tract infection (UTI) with carbapenem-resistant (CR) Klebsiella pneumoniae (Kpn) and the antibiotic resistance spectrum of the strains in patients. As secondary objectives, we elaborated the profile of these patients and the incidence of different types of carbapenemases. Methods: We conducted a retrospective case-control study in which we compared a group of 62 patients with urinary tract infections with CR Kpn with a control group consisting of 136 patients with urinary tract infections with multidrug-resistant (MDR), but carbapenem-sensitive (CS), Kpn, who were hospitalized between 1 January 2022 and 31 March 2024. Results: Compared to patients with urinary tract infections with CS Kpn, patients with urinary tract infections with CR Kpn were preponderant in rural areas (62.9% vs. 47.1%, p = 0.038) and more frequently had an upper urinary tract infection (69.4% vs. 36.8%, p < 0.01). Among the risk factors examined, patients in the study group had a higher presence of urinary catheters inserted for up to one month (50% vs. 34.6%, p = 0.03), rate of hospitalization in the last 180 days (96.8% vs. 69.9%, p < 0.01) and incidence of antibiotic therapy in the last 180 days (100% vs. 64.7%, p < 0.01). They also had a higher rate of carbapenem treatment in the last 180 days (8.1% vs. 0%, p < 0.01). Patients in the study group had a broader spectrum of resistance to all antibiotics tested (p < 0.01), with the exception of sulfamethoxazole–trimethoprim, where the resistance rate was similar in both groups (80.6% vs. 67.6%, p = 0.059). In the multivariate analysis, transfer from other hospitals (OR = 3.51, 95% and CI: 1.430–8.629) and treatment with carbapenems in the last 180 days (OR = 11.779 and 95% CI: 1.274–108.952) were factors associated with an increased risk of disease compared to the control group. The presence of carbapenemases was observed in all patients with CR Kpn, in the order of frequency New Delhi metallo-ß-lactamase (NDM) (52.2%), Klebsiella pneumoniae carbapenemase (KPC) (32.6%), and carbapenem-hydrolyzing oxacillinase (Oxa-48) (15.2%). Conclusions: The environment of origin and previous treatment with carbapenems appear to be the factors associated with an increased risk of urinary tract infection with CR Kpn compared to patients with urinary tract infections with CS Kpn. CR Kpn exhibits a broad spectrum of antibiotic resistance, among which is resistance to carbapenem antibiotics.