In London, IAG stock is down more than 20% while shares of the company trading in Madrid are down 25%.
However, the Brexit may pose an even greater and more complicated issue for IAG.
Even though IAG's operating headquarters is in London, the company is actually registered in Spain.
This is arrangment that worked well for the company that formed following the 2011 merger of British Airways and Spain's national airline Ibera.
But with Britain's decision to detach itself from the EU, IAG could be left in a precarious state should the incoming nationalistic UK government impose foreign ownership restrictions on British airlines.
Foreign ownership restrictions for airlines are customary around the world. For instance, the US limits foreign ownership to 25% while the EU's cap is at 49%. Since British Airways is now 100% owned by an EU (foreign) company, IAG may be put in a position where it will have to divest it's holdings .
Oddly enough, IAG was very fortunate that it decided to register in Spain instead of the UK. Had the company registered in Britain, it would immediately subject to non-EU ownership restrictions. In addition to BA and Iberia, IAG also own Irish national airline Aer Lingus as well as Spanish low-cost carrier Vueling.
In a statement to Business Insider, IAG's CFO Enrique Dupuy de Lome attempted to allay investors' fears over the future of his company.
"INTERNATIONAL CONSOLIDATED AIRLINES GROUP, S.A. (IAG) believes that the vote to leave the European Union will not have a long term material impact on its business. In the short term, however, in the run up to the UK referendum during June, IAG experienced a weaker than expected trading environment. Following the outcome of the referendum, and given current market volatility, while IAG continues to expect a significant increase in operating profit this year, it no longer expects to generate an absolute operating profit increase similar to 2015."
IAG has yet to make any mention of possible foreign ownership restrictions.
According to Airways News senior business analyst Vinay Bhaskara, IAG's ownership stake in British Airways could be a problem, but it depends on how much close economic cooperation the UK is willing to engage in with Europe.
Even if IAG isn't forced to cut back on its British Airways ownership stake, the company still faces some significant headwinds.
Although IAG reported a 14.1% traffic increase in May, the company indicated that business had been slower than expected during the run up to Thursday's referendum.
*The original version of the story mistated the date of IAG's formation. The story has been changed to reflect the correct date which is 2011.