The agreement has yet to be finalised but it handed Spain a diplomatic victory as it still lays claim to the overseas territory which it ceded to Britain in 1713. The EU has warned Britain that issues relating to Britain's departure - such as the size of the divorce bill and residence rights of EU citizens - must be solved before a new trade deal can be discussed.
The territory's chief minister, Fabian Picardo has said he wants a Brexit deal that preserves access to the EU's single market and guarantees that people can freely move across to Spain.
Esteban González Pons, the vice-chairman of the European People's Party, told Spain's El Pais newspaper this omission was "very relevant", adding: "Gibraltar isn't part of the United Kingdom".
Gibraltar faces an uncertain future after Brexit, with Spanish ministers suggesting they'll seek joint sovereignty of the territory.
But, while the new Foreign Minister's comments will provide some comfort to those who have to cross the frontier into Gibraltar to work, CM Picardo has warned that Spain's sovereignty objective remains unchanged.
Beside Gibraltar, the Council guidelines include other United Kingdom border issues affected by Brexit, including between Nothern Ireland and the Republic of Ireland, where "flexible and imaginative solutions will be required", to avoid a hard border, the text says.
Thousands commute between Gibraltar and Spain every day, making open borders a crucial issue of the rock's politics.
The 30,000 British citizens who live there voted 96% to 4% to remain in the European Union in last June's referendum.
The clause was included in the negotiating strategy set out by the European Council on Friday, which also said that the United Kingdom must settle its Brexit bill and agree the future of EU citizens in the United Kingdom before trade deal talks could start.
Theresa May did not refer directly to Gibraltar in her Article 50 letter to Donald Tusk on Wednesday. "We have been firm in our commitment never to enter arrangements under which the people of Gibraltar would pass under the sovereignty of another state against their wishes, nor to enter into a process of sovereignty negotiations with which Gibraltar is not content", she told MPs.
"The whole world and the whole European Union should know: this changes nothing in respect of our continued, exclusive British sovereignty", he said.
Gibraltar is an island off the southern coast of Spain with a population of around 30,000.