COVID-19 vaccinations are recommended for children with cancer but data on their vaccination response is scarce. This study assesses the antibody and T-cell response following a 2- or 3-dose vaccination with BNT162b2 mRNA COVID-19 vaccine in children (5–17 years) with cancer. For the antibody response, participants with a serum concentration of anti-SARS-CoV-2 spike 1 antibodies of >300 binding antibody units per milliliter were classified as good responders. For the T-cell response, categorization was based on spike S1 specific interferon-gamma release with good responders having >200 milli-international units per milliliter. The patients were categorized as being treated with chemo/immunotherapy for less than 6 weeks (Tx < 6 weeks) or more than 6 weeks (Tx > 6 weeks) before the first immunization event. In 46 patients given a 2-dose vaccination series, the percentage of good antibody and good T-cell responders was 39.3% and 73.7% in patients with Tx < 6 weeks and 94.4% and 100% in patients with Tx > 6 weeks, respectively. An additional 3rd vaccination in 16 patients with Tx < 6 weeks, increased the percentage of good antibody responders to 70% with no change in T-cell response. A 3-dose vaccination series effectively boosted antibody levels and is of value for patients undergoing active cancer treatment.