"Our formula... is British-Spanish co-sovereignty for a determined period of time, which after that time has elapsed, will head towards the restitution of Gibraltar to Spanish sovereignty," Spanish Foreign Minister Jose Manuel Garcia-Margallo told Spanish radio.
The tiny rocky outcrop nestled on Spain's southern tip has long been a source of friction between London and Madrid, which wants it back under its control centuries after it was ceded to Britain in 1713.
Spain's conservative government, which has been in place since 2011, has been particularly vocal about its desire to see Gibraltar come back into its fold, and the Rock is worried that Brexit will leave it at the mercy of Madrid.
Margallo said the issue of Gibraltar was no longer within the remit of the European Union.
"It is now a bilateral issue that will be negotiated exclusively between the United Kingdom and Spain," he added, saying a solution would have to be found if Gibraltar wanted to keep its access to the EU's single market.
The Rock, as it is known, relies in large part on access to the single market for its thriving economy.
In a tweet, Gibraltar's Chief Minister Fabian Picardo, who called a crisis cabinet meeting on Friday morning, called for calm.
We have surpassed greater challenges. It is time for unity, for calm & for rational thinking. Together & united we will continue to prosper.— Fabian Picardo (@FabianPicardo) June 24, 2016
Gibraltar, the tiny British Overseas Territory at the foot of Spain was the first to declare its result. And it was the least surprising of all the EU referendum vote counts.
Gibraltar voted overwhelmingly (96 percent) in favour of Britain remaining in the European Union with 96 percent. With a turnout of 84 percent, 19,322 checked the box to stay in the EU and a mere 823 voted to leave.
On Friday morning, fueled by Garcia Margallo's comments, #GibraltarEspañol was trending on Twitter.
Spanish workers on the other side of the border, many of whom depend on jobs in Gibraltar for their livelihood, reacted with "a lot of concern and fear."
The border town of La Linea de la Concepcion is of particular concern.
Unemployment in this 72,000-strong city stands at 40 percent, one of the worst-hit places in Spain, and the majority of those who work do so over the border.
Juan Jose Uceda of the Association of Spanish Workers in Gibraltar said the grouping feared that the "work situation for thousands of Spaniards and foreigners working in Gibraltar will become more difficult."
They fear that the crucial land border crossing to Gibraltar - a long-time flashpoint in the row between the Rock and Spain - could be affected as it has been in the past.
In one particularly belligerent row over disputed waters, Spanish authorities upped border checks in 2013, creating hours-long logjams and forcing the European Commission to wade in and ease the crisis.
But Spain's acting Prime Minister Mariano Rajoy sought to ease their concerns in a televised address.
"With regards to Spanish citizens working in Gibraltar... their rights have not changed," he said.
But those who work in Gibraltar and live in Spain were already voicing their concerns,
Gavin Doughty Spain: Was not expecting that.
"On a personal level my life is going to have drastic changes," Gavin Doughty, a Brit lives in Spain but works in Gibraltar, told the Local.
" got paid today 10 percent less than I would have yesterday and my company's EU passporting rights will only apply for the next two years at most. So besides facing the possibility of being an illegal alien in Spain I am probably going to lose my job too."