The variant's emergence has triggered a strong global response as countries worried that it could spread fast even in vaccinated populations impose travel curbs and other restrictions.
BioNTech SE said it had started work on a vaccine tailored to Omicron, along with partner Pfizer.
Meanwhile, Moderna Inc said it could take months to begin shipping such a vaccine, Chief Executive Officer Stéphane Bancel told CNBC.
Bancel said the effectiveness of existing COVID-19 vaccines against the variant was currently not known, adding there should be more clarity in about two weeks.
Johnson & Johnson is also evaluating the effectiveness of its COVID-19 vaccine against Omicron, while also pursuing a vaccine specific to the variant.
"We have begun work to design and develop a new vaccine against Omicron and will rapidly progress it into clinical studies if needed," said Mathai Mammen, global head of research for J&J's pharmaceuticals unit.
A top South African infectious disease expert said Omicron appears to be more transmissible than previous variants, including to people with immunity from vaccination or prior infection.
(Reporting by Manas Mishra in Bengaluru; Editing by Sriraj Kalluvila)