Meanwhile, protests were held including in Agadir, in the capital, Rabat, and in the commercial capital, Casablanca, where men and women together held up skirts as banners under the slogans "Wearing a dress isn't a crime" and "My dress, my freedom".
The two women have asked for anonymity, saying they are unused to the public spotlight, and have been named in local media only as Sanaa and Siham.
Their lawyer said they were themselves from small, conservative inland towns but had moved to Agadir to work in hairdressing salons.
No photographs have appeared to show exactly what kind of dresses they were wearing, but the apparel of some of the women who attended the protests in their support, wearing sleeveless dresses and knee-length skirts, may give some idea. The police report said the dresses were "tight-fitting".
As with most Muslim countries, it is common but by no means universal or compulsory in Morocco for women to wear a headscarf. Unveiled women in traditional areas - such as a souk in a conservative town - would normally cover their shoulders, arms and legs, but there is no requirement to do so.
There is considerably more latitude in Westernised and tourist areas.
Despite its liberal reputation - derived partly from its history as both a French colony and a haven for Westerners looking for a variety of "alternative lifestyles", ranging from artists to drug-users and even paedophiles - Morocco has faced many of the same difficulties as other Arab countries squaring its society with some effects of modernisation.
In common with many other Arab countries, it has become more conservative in recent years.
