(1): Background: With the recent introduction of vesical imaging reporting and data system (VI-RADS), magnetic resonance imaging (MRI) has become the main imaging method used for the preoperative local staging of bladder cancer (BCa). However, the VI-RADS score is subject to interobserver variability and cannot provide information about tumor cellularity. These limitations may be overcome by using a quantitative approach, such as the new emerging domain of radiomics. (2) Aim: To systematically review published studies on the use of MRI-based radiomics in bladder cancer. (3) Materials and Methods: We performed literature research using the PubMed MEDLINE, Scopus, and Web of Science databases using PRISMA principles. A total of 1092 papers that addressed the use of radiomics for BC staging, grading, and treatment response were retrieved using the keywords “bladder cancer”, “magnetic resonance imaging”, “radiomics”, and “textural analysis”. (4) Results: 26 papers met the eligibility criteria and were included in the final review. The principal applications of radiomics were preoperative tumor staging (n = 13), preoperative prediction of tumor grade or molecular correlates (n = 9), and prediction of prognosis/response to neoadjuvant therapy (n = 4). Most of the developed radiomics models included second-order features mainly derived from filtered images. These models were validated in 16 studies. The average radiomics quality score was 11.7, ranging between 8.33% and 52.77%. (5) Conclusions: MRI-based radiomics holds promise as a quantitative imaging biomarker of BCa characterization and prognosis. However, there is still need for improving the standardization of image preprocessing, feature extraction, and external validation before applying radiomics models in the clinical setting.