Assistant Inspector Obert Magebede (38) was arrested in Harare last week after his nephew reported the alleged abuse to police.
"There has been a trend in the media to equate sodomy with rape,” said the organisation.
“This is alarming because it promotes the dangerous myth that homosexual men are automatically rapists and abusers of children."
GALZ condemned the actions of the police officer but said that the country’s sodomy laws incorrectly lump gay people with rapists. It noted that the officer has been charged with three counts of aggravated indecent assault instead of rape.
Consensual sodomy must be legalised
"There is no distinction under Zimbabwean law between consensual same sex conduct, which GALZ believes should be decriminalised, and enforced sodomy that should be re-termed rape."
It added: "Thinking on sodomy in Zimbabwean society is muddled and the issues need to be clarified in order that justice be done.
“Sodomy per se is not wrong or harmful to society but rape, sexual abuse, physical violence, abuse of authority and sexual relations between adults and minors are criminal acts and it is correct that they be punishable by law."
The organisation blamed cultural taboos around sex in Zimbabwean society for not permitting children to be properly informed about sexuality and the dangers of sexual predators.
It also called for a review of sodomy laws by decriminalising consensual sodomy and replacing the term ‘enforced sodomy’ with rape.
"Only then can justice be done in this country," said GALZ.