Background: Chronic kidney disease (CKD) is a common complication of a non-kidney solid organ transplant (NKSOT). Identifying predisposing factors is crucial for an early approach and correct referral to nephrology. Methods: This is a single-center retrospective observational study of a cohort of CKD patients under follow-up in the Nephrology Department between 2010 to 2020. Statistical analysis was performed between all the risk factors and four dependent variables: end-stage renal disease (ESKD); increased serum creatinine ≥50%; renal replacement therapy (RRT); and death in the pre-transplant, peri-transplant, and post-transplant periods. Results: 74 patients were studied (7 heart transplants, 34 liver transplants, and 33 lung transplants). Patients who were not followed-up by a nephrologist in the pre-transplant (p < 0.027) or peri-transplant (p < 0.046) periods and those who had the longest time until an outpatient clinic follow-up (HR 1.032) were associated with a higher risk of creatinine increase ≥50%. Receiving a lung transplant conferred a higher risk than a liver or heart transplant for developing a creatinine increase ≥50% and ESKD. Peri-transplant mechanical ventilation, peri-transplant and post-transplant anticalcineurin overdose, nephrotoxicity, and the number of hospital admissions were significantly associated with a creatinine increase ≥50% and developing ESKD. Conclusions: Early and close follow-up by a nephrologist was associated with a decrease in the worsening of renal function.