DNA aptamers are versatile molecular species obtained by the folding of short single-stranded nucleotide sequences, with highly specific recognition capabilities against proteins. Here we test the ability of DNA aptamers to interact with the spike (S-)protein of the SARS-CoV-2 viral capsid. The S-protein, a trimer made up of several subdomains, develops the crucial function of recognizing the ACE2 receptors on the surface of human cells, and subsequent fusioning of the virus membrane with the host cell membrane. In order to achieve this, the S1 domain of one protomer switches between a closed conformation, in which the binding site is inaccessible to the cell receptors, and an open conformation, in which ACE2 can bind, thereby initiating the entry process of the viral genetic material in the host cell. Here we show, by means of state-of-the-art molecular simulations, that small DNA aptamers experimentally identified can recognize the S-protein of SARS-CoV-2, and characterize the details of the binding process. We find that their interaction with different subdomains of the S-protein can effectively block, or at least considerably slow down the opening process of the S1 domain, thereby significantly reducing the probability of virus-cell binding. We provide evidence that, as a consequence, binding of the human ACE2 receptor may be crucially affected under such conditions. Given the facility and low cost of fabrication of specific aptamers, the present findings could open the way to both an innovative viral screening technique with sub-nanomolar sensitivity, and to an effective and low impact curative strategy.