Alfonso Dastis insisted however that Madrid and London resolve "small irritating problems" before allowing any post-Brexit deal to be applied to the tiny rocky outcrop nestled on Spain's southern tip.
Gibraltar has been under British control since 1713 but Madrid has long wanted it back.
As such, authorities in the territory fear Spain will influence the complex negotiations between the EU and Britain over its departure from the bloc to try to gain authority over Gibraltar or complicate daily life there.
"Nothing will change" after Britain leaves, Dastis told AFP, adding that Brexit would not affect the daily to-and-fro between the two sides, crucial for the livelihood of thousands of workers who make the land crossing to Gibraltar every day, and for the economy of the territory itself.
"People will be able to keep living in one place and working in another," he added.
"We don't have any intention of making life difficult for people, or closing any barriers or complicating mobility."
The small land border between Spain and Gibraltar is a longtime flashpoint in the row.
Spain's dictator Francisco Franco went as far as closing the crossing in 1969, all but stranding inhabitants who had to rely on air and boat links until it was fully reopened in 1985.
Relations have ebbed and flowed since, but the past years have seen a regain in tension under Spain's conservative government, which apart from sovereignty claims also bristles at tobacco smuggling across the border and accuses Gibraltar of being a corporate tax haven.
Spain caused a stir last year when it had a clause inserted into the EU's negotiating position stating that post-Brexit, Spain will have the right to veto any future relationship between the 27-member bloc and Gibraltar.
This clause caused huge tensions when it was unveiled in March 2017, prompting British Prime Minister Theresa May to say she would "never" allow Gibraltar to slip from British control against the wish of Gibraltarians.
Dastis said that Spain would not make its desired recovery of Gibraltar a condition in Brexit talks.
"We're very interested in maintaining the close relationship we have with the United Kingdom, which we want to improve in terms of people-to-people exchanges and in terms of investment," he said.
But he insisted that Spain and Britain would have to resolve "small irritating problems" between the two before allowing the post-Brexit deal to be applied to Gibraltar.
These include the issue of Gibraltar's airport, which is built on a piece of land between Spain and the Rock that was not ceded to Britain in 1713.
As such, Dastis said Spain would like joint use of the airport.
He also said there was "a problem in the exchange of tax information" -- a claim Gibraltar denies, saying it regularly complies to Spanish requests for data.