The Scottish Government pilot scheme, which is backed by funding of £42,500, will be run by Community Food Initiatives North East (CFINE), a social enterprise focused on improving health and wellbeing for those in poverty.
At least 1,000 women and girls from low-income homes will benefit from the sixth-month scheme.
It is thought to be the first national government-sponsored scheme of its kind, according to The Scotsman.
Equalities Secretary Angela Constance said it was ‘unacceptable’ that some women and girls in Scotland are unable to access sanitary products.
She added: ‘That is why, as part of our wider aims to eradicate poverty from our country, we are exploring how to make products freely available to low-income groups.
‘The pilot in Aberdeen is a first step to help us understand the barriers women and girls face – and to help us develop a sensitive and dignified solution to making these products easily accessible to those who need them.’
Labour MSP Monica Lennon, who has been a vocal campaigner on the issue of period poverty, said the move was welcome but did not go far enough.
She added: ‘I’m pleased the campaign I have started as an opposition MSP has pushed SNP ministers to act but the reality is that women and girls urgently need national action now.