Olfactory dysfunction is common in COVID-19, and sudden-onset dysosmia is an early marker for wild-type SARS-CoV-2 infection. Over 10 000 mutations of SARS-CoV-2 have been registered, with variants of concern (VOC) under particular scrutiny. We report a telemedicine-based, multicentre, prospective cohort study with quantitative olfaction testing comparing 79 patients with a confirmed VOC-Delta (n = 21) or wild-type (WT) SARS-CoV-2 infection. Acute SARS-CoV-2 infection led to significant decrease of olfactory function in both cohorts. A majority of patients suffered from hyposmia or anosmia at inclusion with only 26 individuals performing normosmic. Sniffin'Sticks total scores were significantly higher for VOC-Delta patients at onset of illness, compared to WT patients (p < 0.001). At 4 weeks follow-up, olfaction scores recovered only partially for WT patients, thus odds of recovery were stronger in VOC-Delta patients. Also, subjective self-rating of chemosensory function was lower in WT, compared to VOC-Delta patients. The need for ongoing olfaction studies and their prognosis in SARS-CoV-2 background remains urgent, also in the light of increasing numbers of olfaction-related patient presentations.