Background and Objectives: The prospective study was conducted to evaluate humoral and cellular immune responses after two doses of BNT162b2 (Pfizer-BioNTech) vaccine and possible relation with other factors (medication, etc.) in kidney transplant patients. Materials and Methods: Out of 167 vaccinated patients, 136 agreed to a follow-up visit three to six weeks after vaccination. Results: Only 39 patients (29%) developed antibody response against SARS-CoV-2 (≥35.2 binding antibody units (BAU)/mL) after full vaccination. Multivariate binary logistic regression analysis showed that predictive factors for good antibody response to the COVID-19 vaccine were better kidney function, higher hemoglobin level, and no use of mycophenolate mofetil for immunosuppression. For seropositive kidney transplant patients there was a significant negative correlation between anti-SARS-CoV-2 antibody titer and CD4/CD8 ratio (Spearman’s correlation coefficient −0.4, p = 0.02), percentage of CD19+ cells (r = −0.37, p = 0.02), and a positive correlation with percentage of CD8+ cells (r = 0.4, p = 0.01). There was an increase of total leucocyte count after vaccination in the total studied population, and in the group of responders. Conclusions: Only one third of kidney transplant patients develop sufficient antibody responses after full COVID-19 vaccination with Pfizer-BioNTech. Better kidney function, higher hemoglobin level, and no use of mycophenolate mofetil for immunosuppression increases the adequacy of response. The antibody titers correlated positively with relative number of CD8+ cells and negatively with CD4/CD8 ratio in responders.