Mr Botin reportedly bought the painting in 1977 at the Marlborough Fine Art Fair in London for his personal collection.
He has a stake in the company that owns the yacht where the painting was found but "was not on board at the time".
The seizure is the latest chapter in a three-year battle by the 79-year-old billionaire, Spain's 15th richest man according to Forbes, to take the Picasso out of Spain and auction it off in London.
Mr Botin, who was Santander's vice president from 1999 to 2004, made a formal request in 2012 via Christie's Iberia to definitively transfer the work from Spain to London.
That request was denied by the Spanish culture ministry on the grounds that there was "no other similar work on Spanish soil".
Mr Botin appealed the decision, arguing that the work was not technically in Spain anyway as it was hanging in a 65-metre superyacht Adix moored at the Valencia Royal Nautical Club under a British flag, and was thus under British law.
He also argued he was not the direct owner, as the work was the property of the Panamanian Society Euroshipping Charter Company of which he is the largest shareholder.
The appeal was quashed with judges citing the 1982 Montego Bay Convention and stating that "the existence of a ship in a Spanish port, except in the case of military vessels, is subject to Spanish law".
An attempt to export the painting to Switzerland on Thursday "drew the attention of French officials", France's customs authority said, with agents boarding the boat in the port of Calvi the following day.
According to Corsicanetinfo, the painting was due to be transferred to a specially-chartered private jet from Spain due to land at 11am in Calvi-Balagne airport last Friday "with no passengers on board".
It was then due to leave an hour later with a "package" but no passengers for Switzerland but the flight was "cancelled at the last minute".
The work was thought to be seized from the Adix, as shipping records show that the a 14-crew, 64.85m-long schooner left Valencia in June and stopped off at Menorca before arriving off the coast of Corsica on 10 July. The vessel's current position is off the Anse de Chevanu in southern Corsica.
The ship's captain could only produce two documents regarding the work of art, the statement said - one of which was a May 2015 Spanish court ruling confirming that the painting was "a national treasure (which) could under no circumstances be taken out of Spain".
The painting comes from Picasso's so-called "Gósol period".
Picasso, arguably the famous native of the southern Spanish city of Malaga, lived in the town of Gósol, in Catalonia, in the summer of 1906 and produced various works which influenced Cubism.
"There is no similar work that exists in Spain, making this work one of the few paintings produced by the painter during what is known as the Gósol period, the discoveries at this time strongly influenced not only Cubism but the subsequent evolution of 20th century painting," Spain's Board of Classification, Valuation and Export of Spanish historical patrimony advised at the time.
French customs officials are now awaiting an official Spanish request to recover the painting.
The market for Picasso paintings reached new heights in May when Les femmes d'Alger (Version O) smashed the world record for a painting sold at auction, fetching a fraction over $179 million (£116m) in New York.
Brooke Lampley, the head of Impressionist and Modern Art at Christie's, said before the auction: "There is an incredible thirst in the market right now for top-quality works by renowned artists. Pablo Picasso is the most highly recognised figure in the art world today and this piece is in many ways the culmination of his career."
In February, a Picasso stolen from the Pompidou Centre in Paris was found by a US customs official after it was posted across the Atlantic disguised as a cheap Christmas present.
La Coiffeuse (The Hairdresser), painted in 1911, was reported stolen in 2001 when it was discovered missing from the Paris museum.
It lay hidden for the next 14 years until it turned up in Newark in December in a FedEx package from Belgium, labelled as "art craft/toy" with a stated value of $37 and with the message "Joyeux Noel" (Happy Christmas).
