(1) Background: triple-negative breast cancer (TNBC) remains a clinical and therapeutic challenge primarily affecting young women with poor prognosis. TNBC is currently treated as a single entity but presents a very diverse profile in terms of prognosis and response to treatment. Positron emission tomography/computed tomography (PET/CT) with 18F-fluorodeoxyglucose ([18F]FDG) is gaining importance for the staging of breast cancers. TNBCs often show high [18F]FDG uptake and some studies have suggested a prognostic value for metabolic and volumetric parameters, but no study to our knowledge has examined textural features in TNBC. The objective of this study was to evaluate the association between metabolic, volumetric and textural parameters measured at the initial [18F]FDG PET/CT and disease-free survival (DFS) and overall survival (OS) in patients with nonmetastatic TBNC. (2) Methods: all consecutive nonmetastatic TNBC patients who underwent a [18F]FDG PET/CT examination upon diagnosis between 2012 and 2018 were retrospectively included. The metabolic and volumetric parameters (SUVmax, SUVmean, SUVpeak, MTV, and TLG) and the textural features (entropy, homogeneity, SRE, LRE, LGZE, and HGZE) of the primary tumor were collected. (3) Results: 111 patients were enrolled (median follow-up: 53.6 months). In the univariate analysis, high TLG, MTV and entropy values of the primary tumor were associated with lower DFS (p = 0.008, p = 0.006 and p = 0.025, respectively) and lower OS (p = 0.002, p = 0.001 and p = 0.046, respectively). The discriminating thresholds for two-year DFS were calculated as 7.5 for MTV, 55.8 for TLG and 2.6 for entropy. The discriminating thresholds for two-year OS were calculated as 9.3 for MTV, 57.4 for TLG and 2.67 for entropy. In the multivariate analysis, lymph node involvement in PET/CT was associated with lower DFS (p = 0.036), and the high MTV of the primary tumor was correlated with lower OS (p = 0.014). (4) Conclusions: textural features associated with metabolic and volumetric parameters of baseline [18F]FDG PET/CT have a prognostic value for identifying high-relapse-risk groups in early TNBC patients.