The report recommends that "language and learning about periods is inclusive of all genders, cultures, faiths and sexual orientations. For example; 'girls and women and others who have periods'".
Brighton & Hove City Council said in a statement: "By encouraging effective education on menstruation and puberty, we hope to reduce stigma and ensure no child or young person feels shame in asking for period products inside or outside of school if they need them.
"We believe that it's important for all genders to be able to learn and talk about menstruation together… Our approach recognises the fact that some people who have periods are trans or non-binary."
The same council also recently released a "Trans Inclusion Schools Toolkit" to help teachers treat gender identity sensitively.
It asks teachers to be respectful and inclusive of children who are questioning their gender, and tells them that purposefully not referring to children by their preferred pronoun or name can constitute harassment.
The toolkit also recommends schools adopt a non-gendered uniform so all children feel included, and to reduce bullying.
Tory MP David Davies told The Mail on Sunday that it was "insanity" for teachers to tell pupils that transgender boys can have periods.
He said: "Learning about periods is already a difficult subject for children that age, so to throw in the idea girls who believe they are boys also have periods will leave them completely confused."
However, leading doctors have previously recommended that primary school children are taught about LGBT issues.
Earlier this year, the Royal College of Paediatricians and Child Health (RCPCH) urged minister go further in their guidance on sex and relationship classes, which will become compulsory from 2020.
Draft Government recommendations say schools are free to determine how they address lesbian, gay, bisexual and transgender (LGBT) issues, ensuring teaching is "sensitive and age-appropriate".
The Royal College said: "There needs to be a clear statement that LGBT people and relationships are part of teaching about healthy relationships in primary school. This can be demonstrated in relation to families - but also it is helpful to children to learn the meaning of terms such as lesbian, gay and bisexual".