In our previous research, a series of phenylsulfonylfuroxan-based hydroxamates were developed, among which compound 1 exhibited remarkable in vitro and in vivo antitumor potency due to its histone deacetylase (HDAC) inhibitory and nitric oxide (NO)-donating activities. Herein, the in-depth study of compound 1 revealed that this HDAC inhibitor-NO donor hybrid could enduringly increase the intracellular levels of acetyl histones and acetyl α-tubulin, which could be ascribed to its irreversible inhibition toward class I HDACs and HDAC6. Structural modification of compound 1 led to a novel phenylsulfonylfuroxan-based hydroxamate 4, which exhibited considerable HDAC6 inhibitory activity and selectivity. Furthermore, compound 4 could inhibit intracellular HDAC6 both selectively and irreversibly. To the best of our knowledge, this is the first research reporting the irreversible inhibition of HDAC6. It was also demonstrated that compared with ACY-241 (a reversible HDAC6 inhibitor in clinical trials), the irreversible HDAC6 selective inhibitor 4 exhibited not only superior anti-multiple myeloma activity but also improved therapeutic index.