Representatives of the German environmental group OceanCare and the online activist site Avaaz handed the petition to Spain's environment ministry on Monday.
The petition signed by 180,610 EU citizens calls on the ministry to "stop the imminent petrol prospecting off the Balearic coast".
OceanCare argues the noise created by the drilling is "so extreme that it poses a mortal threat to whales, dolphins and other marine species in the region".
The drilling — which produces 10 to 15 second bursts of intense noise — is also a risk to the all-important tourism industry of islands including Majorca and Ibiza, Avaaz said.
"Using compressed air cannons to look for oil in Ibiza and Majorca is like playing Russian roulette with natural and economic resources," said Avaaz campaign coordinator Christoph Schott on Monday.
Of all the advanced economies of the OECD grouping, Spain is the most reliant on energy imports, buying in 99.9 percent of its oil and gas.
But the Spanish government is hoping to combat this by prospecting for oil and gas off the Balearic and Canary Islands.
In the Balearic Islands, the company Capricorn Spain Limited, a subsidiary of the Scottish energy group Cairn, is carrying out environmental impact studies with a view to probing for oil.
In the Canary Islands, Spanish energy giant Repsol has announced it hopes to start exploratory drilling in October, despite the objections of regional president Aurino Rivero.
WWF has called for a whale sanctuary to protect what it calls a unique area, home to "nearly a third of the cetacean species on the planet".
But Spain's industry minister José Manuel Soria has said the country can't "afford the luxury" of not drilling for oil and gas off the coast of the Canary Islands.
He has also highlighted that the unemployment rate in the archipelago stands at a worrying 33 percent, 8 percent higher than the national average.