According to The Mirror, one fan counted eight German supporters wearing black make-up and posted a picture on Instagram of the offensive acts.
A FIFA spokesperson later revealed that the governing body's "zero-tolerance rules" will be in force and called on any spectator who has evidence to come forward.
She said: "If something like a banner is spotted, it will be. If something is not spotted and someone has images of it, then if anyone submits evidence of those things then our disciplinary committee will consider it.
"We clearly have zero tolerance of any form of discrimination."
The probe comes after European anti-discrimination network Fare lodged a complaint with FIFA over the display of neo-Nazi banners by Russian and Croatian fans during previous games.