In this brief communication we are showing original research results with early estimates from Danish nationwide databases of vaccine effectiveness (VE) against the novel SARS-CoV-2 Omicron variant (B.1.1.529) up to five months after a primary vaccination series with the BNT162b2 or mRNA-1273 vaccines. Our study provides evidence of protection against infection with the Omicron variant after completion of a primary vaccination series with the BNT162b2 or mRNA-1273 vaccines; in particular, we found a VE against the Omicron variant of 55.2% (95% confidence interval (CI): 23.5 to 73.7%) and 36.7% (95% CI: 69.9 to 76.4%) for the BNT162b2 and mRNA-1273 vaccines, respectively, in the first month after primary vaccination. However, the VE is significantly lower than that against Delta infection and declines rapidly over just a few months. The VE is re-established upon revaccination with the BNT162b2 vaccine (54.6%, 95% CI: 30.4 to 70.4%).