In molecular biology, understanding the functional and structural aspects of DNA requires sequence-specific DNA binding probes. Especially, sequence-specific fluorescence probes offer the advantage of real-time monitoring of the conformational and structural reorganization of DNA in living cells. Herein, we designed a new class of D2A (one-donor-two-acceptor) near-infrared (NIR) fluorescence switch-on probe named quinone cyanine–dithiazole (QCy–DT) based on the distinctive internal charge transfer (ICT) process for minor groove recognition of AT-rich DNA. Interestingly, QCy–DT exhibited strong NIR-fluorescence enhancement in the presence of AT-rich DNA compared to GC-rich and single-stranded DNAs. We show sequence-specific minor groove recognition of QCy–DT for DNA containing 5′-AATT-3′ sequence over other variable (A/T)4 sequences and local nucleobase variation study around the 5′-X(AATT)Y-3′ recognition sequence revealed that X = A and Y = T are the most preferable nucleobases. The live cell imaging studies confirmed mammalian cell permeability, low-toxicity and selective staining capacity of nuclear DNA without requiring RNase treatment. Further, Plasmodium falciparum with an AT-rich genome showed specific uptake with a reasonably low IC50 value (<4 µM). The ease of synthesis, large Stokes shift, sequence-specific DNA minor groove recognition with switch-on NIR-fluorescence, photostability and parasite staining with low IC50 make QCy–DT a potential and commercially viable DNA probe.