We discuss constraints on the coefficient A_{MSW} which is introduced to simulate the effect of weaker or stronger matter potential for electron neutrinos with the current and future solar neutrino data. The currently available solar neutrino data leads to a bound A_{MSW} = 1.47^{-0.42}_{+0.54} (^{-0.82}_{+1.88}) at 1\sigma (3\sigma) CL, which is consistent with the Standard Model prediction A_{MSW} = 1. For weaker matter potential (A_{MSW} < 1), the constraint which comes from the flat ^8B neutrino spectrum is already very tight, indicating the evidence for matter effects. Whereas for stronger matter potential (A_{MSW} > 1), the bound is milder and is dominated by the day-night asymmetry of ^8B neutrino flux recently observed by Super-Kamiokande. Among the list of observable of ongoing and future solar neutrino experiments, we find that (1) an improved precision of the day-night asymmetry of ^8B neutrinos, (2) precision measurements of the low energy quasi-monoenergetic neutrinos, and (3) the detection of the upturn of the ^8B neutrino spectrum at low energies, are the best choices to improve the bound on A_{MSW}.