Here, we report DNA-based synthetic nanostructures decorated with enzymes (hereafter referred to as DNA-enzyme swimmers) that self-propel by converting the enzymatic substrate to the product in solution. The DNA-enzyme swimmers are obtained from tubular DNA structures that self-assemble spontaneously by the hybridization of DNA tiles. We functionalize these DNA structures with two different enzymes, urease and catalase, and show that they exhibit concentration-dependent movement and enhanced diffusion upon addition of the enzymatic substrate (i.e., urea and H2O2). To demonstrate the programmability of such DNA-based swimmers, we also engineer DNA strands that displace the enzyme from the DNA scaffold, thus acting as molecular "brakes" on the DNA swimmers. These results serve as a first proof of principle for the development of synthetic DNA-based enzyme-powered swimmers that can self-propel in fluids.