The women say the doctors and nurses should have informed them properly about what was happening.
The rights group representing them, the Legal Assistance Centre, says it has documented 15 cases of alleged HIV sterilisation in hospitals since 2008.
A march in their support is taking place in Windhoek as the case begins.
The BBC’s Frauke Jensen in the capital, Windhoek, says there will also be a sit-in protest at one of the hospitals where the alleged sterilisations took place.
The women want 1m Namibian dollars ($130,000, £90,000) in compensation from the health ministry, our reporter says.
The Legal Assistance Centre says the High Court has granted that women’s identities should not be revealed as they fear "further discrimination and stigmatisation because of their HIV status".
As well as the march in Windhoek, other solidarity marches are planned on Tuesday in South Africa, Zambia, the UK and the US.
Source: BBC