The mainstreaming of genomic medicine requires that non-genetics physicians take on responsibility for genomic medicine tasks. However, previous studies indicate that physicians without formal competence in genetics often lack the experience, knowledge and means to do so. This study assessed the current practice of genomic medicine among Swedish non-genetics physicians (n = 133) using a survey designed by McClaren et al. (McClaren et al. 2020). 67.7% of respondents had been in contact with their regional genetics services during the last year, a majority of which having been so at least monthly. Somewhat fewer, 57.1%, had ordered a gene panel, exome or whole genome during the last year. About a third reported that financing can be a barrier to ordering tests. Only 37.6% reported feeling sufficiently prepared for working with genomic medicine in general, with greatest confidence levels found for taking the medical history. Only a third of participants expected that further developments within genomic medicine will affect their own ways of working. In comparison with previous Australian and UK studies using the same survey, Swedish physicians have more contact with regional genetics services, whereas proportions ordering tests and feeling sufficiently prepared for working with genomic medicine are comparable. Interestingly, Swedish physicians seem less prepared to take on increased responsibilities for genomic medicine than their international peers. We encourage researchers in other countries to use the same survey to allow for further international comparisons to inform policy.