UK and other non-EU investors will lose voting rights when new Brexit trading rules come into force on 1 January.
By law, airlines operating flights in the EU must be owned by citizens of the EU or other affiliated countries.
Ryanair said it was banning its UK shareholders from attending or taking part in its general meetings.
Wizz Air said that if it did not take action, about 80% of its shares would be held by non-EU nationals. It said about 60% of its shareholder base would be sent restricted share notices.
Ryanair said in a statement to the London stock exchange: “These resolutions will remain in place until the board of the company determines that the ownership and control of the company is no longer such that there is any risk to the airline licences.”
The airline said it will not require British citizens to sell their shares, but will ban them from showing up to, speaking at or voting at shareholder meetings.
Another airline, easyJet, has already said it will restrict voting rights for some shareholders to ensure EU citizens own 50% of the company.
A spokesperson for Airlines UK, the trade body for UK-registered airlines, said it was still “working through some of the wider detail” of the Brexit deal.
However, the spokesperson added: “The headline position is that all air travel between the UK and EU – which represents the vast majority of flying by UK carriers – is safeguarded from 1 January, which is good news for holidaymakers, our inbound tourism industry and UK business.”