What we are going to do is apply to British tourists who go to the Balearic islands the same requirements we make of other European citizens, Mr Sanchez told Cadena SER radio.
They will need a full dose of vaccine or a negative PCR, he added, referring to a type of test for the coronavirus.
The new rules will come into force within 72 hours, Mr Sanchez said, without specifying a day.
The move was needed because of a worrying rise in infections in the United Kingdom, TVE quoted him as saying.
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Spain had previously decided to lift the requirement for UK travellers to present a negative PCR test from May 20.
Authorities in Mallorca, a popular holiday destination for Spaniards and foreigners alike, are investigating a coronavirus outbreak involving more than 600 students.
It comes as UK holidaymakers arriving in Portugal who are not fully vaccinated against Covid-19 must quarantine for 14 days on arrival.
Anyone travelling to mainland Portugal by air, land or sea, from Monday, will have to confirm they are fully vaccinated at least two weeks ago or have to isolate.
The new rules were introduced by the Portuguese government and will last until at least July 11.
They said the decision may be revised at any time, depending on the evolution of the epidemiological situation.
The rule does not apply in Madeira, which has been moved back to the UKs green list.
Malta will also only allow those who are fully vaccinated to enter the country without having to quarantine.
The Maltese government will impose the new restrictions from June 30 in response to rising cases of the Delta variant in the UK.
Meanwhile, Germany will on Monday launch an attempt to ban British travellers from the EU, including those who are double jabbed.
German chancellor Angela Merkel previously called for a European Union-wide quarantine on British tourists, with Environment Secretary George Eustice criticising the move as not justified.
According to the Times, Ms Merkel wants to designate Britain as a country of concern due to the spread of the Delta variant.
The paper reports that senior European and national officials on the EUs integrated political crisis response committee will discuss the plans.
However, Spain has said they do not plan to back the EU-wide quarantine and are adamant about setting its own border policy.
UK holidaymakers will have to show either a negative PCR test or proof of vaccination
