Background: There is a growing number of people with dementia in minority ethnic groups in Denmark. Support for the increasing number of family carers from minority ethnic groups is crucial, as caring for a relative with dementia may negatively affect the carer’s health and quality of life. The aim of this study was to determine the feasibility of a personalized intervention for family carers from minority ethnic groups. The intervention was a modified version of a culturally sensitive case-management program developed in Australia which had been shown to improve carers’ sense of competence in managing dementia and their mental well-being. Methods: A small pilot trial was used to examine the feasibility and preliminary efficacy of the intervention. Feasibility indicators included data on recruitment, retention, adherence, and fidelity. Acceptability and suitability of the intervention was explored in post-intervention interviews with family carers, and baseline and follow-up scores for outcome measures were examined. Results: Ten (30%) of 33 eligible family carers consented to participate in the study, but three were lost to follow-up and seven (70%) family carers completed the trial. Intervention fidelity, acceptance, and satisfaction were high. Results for outcome measures indicated that the intervention may improve family carers’ sense of competence by helping them cope better with challenges relating to caring and managing dementia and improved their satisfaction with primary care services. Conclusions: The results suggest that the intervention is feasible and worth exploring for family carers of people with dementia from minority ethnic groups in Denmark.