To understand better enzyme/DNA interactions and to design innovative detectors based on DNA nanoarrays, we need to study the effect of nanometric confinement on the biochemical activity of the DNA molecules. We focus on the study of the restriction enzyme reactions (DpnII) within DNA nanostructures on flat gold films by atomic force microscopy (AFM). Typically we work with a few patches of DNA self assembled monolayers (SAMs) that are hundred nm in size and are lithographically fabricated within alkylthiol SAMs by AFM nanografting. We start by nanografting a few patches of a single-stranded DNA (ssDNA) molecule of 44 base pairs (bps) with a 4 bps recognition sequence (specific for DpnII) in the middle. Afterwards, reaction-ready DNA nanopatches are obtained by hybridization with a complementary 44bps ssDNA sequence. The enzymatic reactions were carried out over nanopatches with different density. By carrying out AFM height measurements, we are able to show that the capability of the DpnII enzyme to reach and react at the recognition site is easily varied by controlling the DNA packing in the nanostructures. We have found strong evidence that inside our ordered DNA nanostructures the enzyme (that works as a dimer) can operate down to the limit in which the space between adjacent DNA molecules is equal to the size of the DNA/enzyme complex. Similar experiments were carried out with a DNA sequence without the recognition site, clearly finding that in that case the enzymatic reaction did not lead to digestion of the molecules. These findings suggest that it is possible to tune the efficiency of an enzymatic reaction on a surface by controlling the steric hindrance inside the DNA nanopatches without vary any further physical or chemical variable. These findings are opening the door to novel applications in both the fields of biosensing and fundamental biophysics.