The report was the first time the SNB published a figure for the environmental impact of the companies in which it holds shares.
The stakes, including in oil majors Chevron Corp and Exxon Mobil, are part of the bank's foreign currency reserves, which stood at 655 billion Swiss francs ($738.28 billion) at the end of 2023.
Last year was the planet's hottest year on record and temperatures remained high at the start of this year.
In Switzerland, the impact was felt as glaciers retreated and many ski resorts have been left without snow after a mild winter.
"The figure of 12 million tons of CO2 equivalents is shocking and far too high," said Asti Roesle of the Climate Alliance Switzerland, which represents over 140 non-governmental groups.
The real scale of the emissions could be three or four times higher once indirect emissions were included, she estimated.
"The SNB is one of the 10 biggest investors in the world, so it can make a difference," Roesle said.
Peter Haberstich, a sustainable finance expert at Greenpeace Switzerland, urged the SNB to encourage companies it has invested in to "reduce their environmental impact".
Where that is not possible, the SNB should divest, he said.
In its report the SNB said it was reducing its own CO2 emissions, and aimed to reach net zero by 2050 at the latest.
But it said it would not change its investment policy, and was not authorised to pursue economic, social or political goals with its investments.
"This also applies to pursuing a plan to reduce the greenhouse gas emissions related to its investments," the SNB said.
"Pursuing objectives other than that of ensuring price stability ... could lead to conflicts of interest, thereby making it more difficult for the SNB to fulfil its mandate."
($1 = 0.8872 Swiss francs)
(Reporting by John Revill; editing by Barbara Lewis)
