In a video the group posted to social media, police officers are seen arresting two protesters as they shouted for "climate justice".
The Sagrada Familia, designed by Catalan architect Antoni Gaudi, is one of Barcelona's main tourist attractions.
Futuro Vegetal slammed what it alleged is insufficient government action on climate change, notably to quell the recent clutch of fires that have caused extensive damage.
The fires have left four people dead and ravaged some 350,000 hectares of land (870,00 acres) in the past fortnight alone, according to the European Forest Fire Information System (EFFIS).
Spain's government called the fires "one of the biggest environmental catastrophes" the country has witnessed in recent memory, and acknowledged a link with climate change.
READ ALSO: Lingering wildfires pile pressure on Spain's PM
This weekend saw the scope of the problem recede, with civil protection services director Virginia Barcones saying Saturday that the emergency was "coming to an end".
Futuro Vegetal, which has links to similar groups abroad, has staged dozens of similar protests, including one in 2022 when they glued their hands to the frames of paintings by Spanish master Francisco de Goya at Madrid's Prado Museum.
Paint was also thrown at a super yacht in Ibiza reportedly belonging to Nancy Walton Laurie, the billionaire heiress of US retail giant Walmart, and a mansion of former FC Barcelona star Lionel Messi in Ibiza.
Spanish police said last year they had arrested 22 members of Futuro Vegetal, including the two who took part in the Prado protest and the group's three main leaders.
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