Green's comments came after Philip Hollobone, another conservative MP, put forward a private member's bill that would restrict people from covering their faces in public.
In addition to proposing the bill, Hollobone said he would refuse to hold meetings with veiled Muslim woman.
Constituents who wear the face veil should either take it off or communicate with him in a "different way" such as mailing a letter, Hollobone said.
Support for ban
A poll released earlier in the week showed that 67 per cent of Britons support a ban on the face veil.
YouGov, an internet-based market research firm, carried out the online survey of 2,205 adults for Five News television.
The Muslim Council of Britain says about 2.5 million Muslims live in the UK and less than one per cent wear a face weil.
The issue of face-covering veils has been debated across Europe.
In France, a ban on the face veil in public passed in the lower house last week and is expected to become law in September.
The bill makes it illegal to cover the face anywhere in public and those caught wearing a full veil would face fines of $190 or be ordered to enrol in a "citizenship course".
France also plans to issue prison sentences and fines to men who force women to wear the face veil.
Critics have said that the ban stigmatises the nation's estimated five million Muslims - the largest Muslim population in western Europe.
They also say it is a political ploy because only an estimated 1,900 women wear the full veil.
Spain and Belgium have similar plans to ban the face veil in public.