Counselling and genetic testing (CGT) after neonatal screening may increase depression and anxiety (DA) levels during cancer surveillance. This study assessed the DA scores in mothers of newborns from Paraná state, Southern Brazil, carrying the TP53 p.R337H variant. To understand and adjust DA conditions during term of pregnancy, we initially detected sociodemographic covariates [marital status (MS), number of children (NC), and/or education level (EL): MS-NC-EL] on an independent group of pregnant women (not subjected to genetic testing). The Hospital Anxiety and Depression Scale (HADS) was used to assess risk factors in pregnant (cross-sectional analysis) and unrelated mothers (at 2-month intervals, longitudinal study) of TP53 p.R337H-tested newborns (three sessions of HADS analysis) using Wilcoxon (Mann–Whitney) and Kruskal–Wallis nonparametric tests. Lower anxiety levels were observed in mothers of noncarriers (without MS-NC-EL = 6.91 ± 1.19; with MS-NC-EL = 6.82 ± 0.93) than in mothers of p.R337H carriers in the first session (without MS-NC-EL = 6.82 = 8.49 ± 0.6025, with MS-NC-EL = 6.82 = 9.21 ± 0.66). The anxiety levels significantly decreased 4 months after CGT (third session) in mothers of p.R337H carriers. We did not find a significant change in depression scores. Mothers with mental health instability requiring medications need periodical psychological support during and after CGT.