Both FA and New Zealand Football said last month that they had not been consulted by global soccer governing body FIFA after reports that Visit Saudi will join international brands such as Adidas, Coca-Cola and Visa as major sponsors.
The 32-team tournament, which kicks off in July, is being co-hosted by Australia and New Zealand. Johnson said FA had consulted on the matter with the government and commercial partners.
"It was an overwhelming consensus that this partnership does not align with our collective vision for the tournament and falls short of our expectations," Johnson said in a statement.
"Whilst the partnership has not been confirmed by FIFA, based on the consultations we have had with our community, key stakeholders and our own position, we would not be comfortable with it.
"While we await further clarity and information as to the details of the partnership from FIFA, we continue to convey this clear message on behalf of Football Australia, New Zealand Football, and our community."
FIFA did not immediately respond to a Reuters request for comment.
Initial reports of the sponsorship deal were met with stinging criticism from several quarters including former players and human rights activists.
Former Australia international and media pundit Craig Foster said the deal would be "disgraceful in the extreme" while veteran US forward Alex Morgan (33) said it 'morally' did not make sense.
Amnesty International Australia said there was an 'irony' in a Saudi tourism body sponsoring the women's tournament as Saudi women "can't even have a job without the permission of your male guardian".
