Serious infections caused by bacteria that are resistant to commonly used antibiotics have become a major global healthcare problem in the 21st century. Multidrug-resistant bacteria causing severe infections mainly grow in complex bacterial communities known as biofilms, in which bacterial resistance to antibacterial agents and to the host immune system is strengthened. As drug resistance is becoming a threatening problem, it is necessary to develop new antimicrobial agents with novel mechanisms of action. Here, we designed and synthesized a small library of N-substituted hydroxylamine (N-HA) compounds with antibacterial activity. These compounds, acting as radical scavengers, inhibit the bacterial ribonucleotide reductase (RNR) enzyme. RNR enzyme is essential for bacterial proliferation during infection, as it provides the building blocks for DNA synthesis and repair. We demonstrate the broad antimicrobial effect of several drug candidates against a variety of Gram-positive and Gram-negative bacteria, together with low toxicity toward eukaryotic cells. Furthermore, the most promising compounds can reduce the biomass of an established biofilm on Pseudomonas aeruginosa, Staphylococcus aureus, and Escherichia coli. This study settles the starting point to develop new N-hydroxylamine compounds as potential effective antibacterial agents to fight against drug-resistant pathogenic bacteria.