The National Trust, which maintains the site, said it did not encourage the defacing of the giant.
Standing at 180ft tall the Cerne Giant is Britain’s largest chalk hill figure.
The new adornment of a flower represents “both the male and the female reproductive parts”, according to the typewritten sheet of paper that was hand-delivered by a woman to Cerne Abbas Stores in Dorset earlier.
“To celebrate International Women’s Day… the aim of this action is to elevate the giant into a human rather than a binary gendered ‘him’,” the written statement continued.
“This temporary enrichment and extension of the penis into flora, is both a proposition for a permanent change to the chalk creation and an invitation to begin peaceful relationships within the sexes by finally creating equality,” it added.
A National Trust spokesman said: “It’s important to celebrate International Women’s Day, but we don’t encourage the defacing of the Cerne Abbas Giant and are very concerned about any interference which may in future encourage damage to this fragile site.
“The giant is protected as both a Scheduled Ancient Monument and as part of a Site of Special Scientific Interest as it’s an important chalk grassland for its wild flowers and the butterflies and wildlife that it supports and is easily damaged.”