Activist group Culture Unstained says the museum is giving "dangerous legitimacy" to the oil company's claim it is aiming for net zero carbon emissions by 2050.
In three press releases published late last week, the museum announced its own target of net zero by 2030 and the new climate change exhibition sponsored by Shell.
Our Future Planet will explore 'carbon capture and storage' techniques that Shell says is "essential for society to reach the goals of the Paris Agreement".
Culture Unstained Co-Director of Campaigns and Research Jess Worth said: "In reality, no oil and gas company is aligned with the targets in the Paris Agreement or is coming close to reducing fossil fuel production as fast as the climate science demands."
Bill McGuire, Professor Emeritus of Geophysical and Climate Hazards at University College London, said it "beggars belief that this iconic British institution has freely chosen to link up with Shell to sponsor their flagship climate exhibition at such a crucial time".
"I can only conclude that they simply don't care, and have no interest whatsoever in playing a responsible role in tackling the climate emergency."