MIT said its algorithm analysed video of a still object to detect "tiny, almost invisible vibrations" that determined how it moved.
The technique, called interactive dynamic video (IDV), does not require any special cameras.
It could be used to create special effects in video games or films.
"This technique lets us capture the physical behaviour of objects, which gives us a way to play with them in virtual space," said Abe Davis, a PhD student at MIT's Computer Science and Artificial Intelligence Laboratory.
Demonstration footage showed a wobbling wire mannequin, playground climbing frame, and a shrub that swayed when virtually tugged.
One potential application for the technology could be to improve the realism in augmented reality games such as Pokemon Go, the research team said.
Pokemon Go superimposes virtual monsters over a live view of the world from a smartphone's camera, although the Pokemon do not interact with real-world objects.
The MIT team has released a video showing how the likes of Pikachu and Snorlax could interact with other real-world objects, using the IDV technique.
Doug James, a professor of computer science at Stanford University, said IDV could also be a useful alternative to traditional animation processes used in the film industry.
Interactive photographs in which still objects can be manipulated have been developed at the Massachusetts Institute of Technology (MIT).