A group of four women claim they have been blocked from registering their #MeToo squad for the event in January 2019.
Organisers told them there is no room for new squads, according to reports.
The procession in Lerwick draws around 1,000 men, dressed as Viking warriors and formed in jarl squads, who parade through the town in one of Scotland’s biggest fire festivals.
The men follow the Guizer Jarl - a form of King - through the streets with the burning of a replica galley boat the climax of the night.
While smaller Up Helly Aa events in Shetland have introduced a female Guizer Jarl, the Lerwick celebration has yet to embrace change.
Zara Pennington, of the Shetland for Up Helly Aa equalities group, said she had responded to advertisement in the Shetland Times calling for registration of squads.
Ms Pennington told the BBC: “There was nothing clearly in the advert that restricted it to previous squads, so we thought it was an opportunity to see how the land lies for whether women would be accepted in squads in Up Helly Aa.”
The group said it was told there was no room for new squads, but it suspects this is an excuse for excluding women, according to the report.
Ms Pennington added: “There might be no new squads but there are existing squads that occasionally take on new members and they’ve neither taken on any women, nor shown any inclination that they would.
“It almost seems to me that unless the committee is giving guidance that existing squads are accepting women, we don’t know the situation and they’ve always refused to comment on this issue.”
The Lerwick event attracts visitors from around the world with Up Helly Aa used to promote Scotland in tourism campaigns.
The event marks the Vikings who used to rule the Shetland islands 1,000 years ago but the Up Helly Aa celebration is a relatively modern invention.
Wild parties in the streets of Lerwick were recorded on Christmas Even in 1824 with burning tar barrels introduced to the festivities around 1840.
It was not until the late 1880s that a Viking long shipappeared with the Guizer Jarl, the chief guizer, not appearing until 1906. The jarl squads were added after World War One and have been a fixture ever since.
In a break with Shetland tradition, the Up Helly Aa celebration on the South Mainland appointed Lesley Simpson as its first female Guizer Jarl three years ago.
Months of planning goes into the Lerwick event with women usually taking up the huge task of sewing and designing costumes and organising the busy post-procession parties in the public halls around Lerwick.
Lerwick Up Helly Aa supporter Emma Williamson told the BBC that she believes most women would not want to take part in the procession.
“If you actually spoke to the women involved and asked ‘do you really want to go out in a squad?’ hand on heart the women I speak to would say no because they have a much better time at the hall,” Ms Williamson said.
Research has found that Viking women may have enjoyed a higher status in Scotland than in other countries colonised by the Norse seafarers.
More Viking women were afforded high-status burials in Scotland when compared to other settlements in Britain and Ireland, it has been claimed.
The Lerwick Up Helly Aa Committee has been contacted for a comment.