Ligand binding to minor-grooves of DNA depends on DNA-base sequence near its binding-site. However, it is not known how base-sequences affect the local solvation of ligand inside minor-grooves of DNA. Here we present a comprehensive study on sequence-dependent solvation dynamics of ligand inside duplex-DNA by measuring the static and dynamic fluorescence Stokes shifts of a popular groove-binder, DAPI, inside DNA minor-grooves created by four different sequences; d(5'-CGCG (AATTC) under bar GCG-3')(2), d(5'CGCG (TTAAC) under bar GCG-3')(2), d(5'-CGCGC (AATTG) under bar CGCG-3')(2,) and d(5'-CGCGC (AATTG) under bar CGCG-3')(2,) having different sequences near DAPI-binding.site. Fluorescence up-conversion and time-correlated single photon counting techniques are employed to capture the dynamic Stokes shifts of DAPI over five decades in time from 100 fs to 10 ns. We show that the ligands sense different static and dynamic solvation inside minor-grooves created by different sequences: Only subtle change in the dynamics is seen in DNA containing -AATTG-, -TTAAG-, and -AATTC- sequences, which show power-law relaxation in initial time-decades, followed by biexponential decay in nanosecond time-scales. However, changing a single base (and the complementary base) near ligand-binding site from -TTAA (G) under bar- to -TTAA (C) under bar- drastically induces the dynamics to follow a single power-law relaxation over the entire five decades. The observed variation of dynamics possibly relate to the local DNA motions, coupled to the hydration dynamics near the ligand-binding site.