JET2 is contacting customers on the Balearic and Canary Islands to ask them to end their package holidays early.
Hundreds of customers have had flights back to the UK cancelled and been asked to leave sooner.
Customers due to return from Spain in early August have been told to return earlier.
However, passengers meant to be flying with the firm on Friday 31 July and Saturday 1 August are not affected - their flights are scheduled as normal.
Several families on holiday on the island of Mallorca, who were due to return next week, have told the BBC they have received emails and text messages telling them they have to return early.
The government has warned against non-essential travel to Spain following a rise in coronavirus cases.
Earlier this week people returning to the UK from Spain were told they would need to quarantine for 14 days.
The travel trade association, ABTA, said FCO advice is issued "for good reason" and travellers need to be aware their travel insurance will be invalid.
Spokesman Jonathan Smith said: "We wouldn't advise that people go against the foreign office travel advice but flights are still operating and people that do choose to go should be aware of the risks involved.
"If they have travel insurance [which they should] then it will most likely be invalidated if anything happens to them while they are on holiday."
Jet2 was approached for a comment.
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