Kidney transplantation is the best option for end-stage chronic kidney disease. Transplant viability is conditioned by drugs’ nephrotoxicity, ischemia–reperfusion damage, or acute rejection. An approach to improve graft survival is the identification of post-transplant renal function prognostic biomarkers. Our objective was to study three early kidney damage biomarkers (N-acetyl-d-glucosaminidase, NAG; neutrophil gelatinase-associated lipocalin, NGAL; and kidney injury molecule-1, KIM-1) in the initial period after transplantation and to identify possible correlations with main complications. We analysed those biomarkers in urine samples from 70 kidney transplant patients. Samples were taken on days 1, 3, 5, and 7 after intervention, as well as on the day that renal function stabilised (based on serum creatinine). During the first week after transplant, renal function improved based on serum creatinine evolution. However, increasing levels of biomarkers at different times during that first week could indicate tubular damage or other renal pathology. A relationship was found between NGAL values in the first week after transplantation and delayed graft function. In addition, higher NAG and NGAL, and lower KIM-1 values predicted a longer renal function stabilisation time. Therefore, urinary NAG, NGAL, and KIM-1 could constitute a predictive tool for kidney transplant complications, contributing to improve graft survival rates.