The Women in Democracy Caucus also wants extra support for women AMs, and more women experts on TV and radio.
Its leader - Presiding Officer Rosemary Butler - said women's voices were "not being heard".
The Welsh government said banning companies from procurement processes would be illegal.
However, a spokesman added: "While we have to recognise this legal constraint, no-one should be in any doubt regarding our dedication to maximising women's participation in all areas of public life."
The report was produced to coincide with International Women's Day.
Dame Rosemary said: "Women's voices are not being heard and our views are being overlooked, so I am working to address the need for more women to apply for and take up public roles and appointments."
Organisations without women on their boards should not be given Welsh government grants or contracts worth over £250,000, a group of AMs has said.