Biological systems use compartmentalisation as a general strategy to control enzymatic reactions by precisely regulating enzyme-substrate interactions. With the advent of DNA nanotechnology, it has become possible to rationally design DNA-based nano-containers with programmable structural and dynamic properties. These DNA nanostructures have been used to cage enzymes, but control over enzyme-substrate interactions using a dynamic DNA nanostructure has not been achieved yet. Here we introduce a DNA origami device that functions as a nanoscale vault: an enzyme is loaded in an isolated cavity and the access to free substrate molecules is controlled by a multi-lock mechanism. The DNA vault is characterised for features such as reversible opening/closing, cargo loading and wall porosity, and is shown to control the enzymatic reaction catalysed by an encapsulated protease. The DNA vault represents a general concept to control enzyme-substrate interactions by inducing conformational changes in a rationally designed DNA nanodevice.