The existence of a light or massive scalar field with a coupling to matter weaker than gravitational strength is a possible source of violation of the weak equivalence principle. We use the first results on the Eötvös parameter by the MICROSCOPE experiment to set new constraints on such scalar fields. For a massive scalar field of mass smaller than 10^{-12} eV (i.e., range larger than a few 10^{5} m), we improve existing constraints by one order of magnitude to |α|<10^{-11} if the scalar field couples to the baryon number and to |α|<10^{-12} if the scalar field couples to the difference between the baryon and the lepton numbers. We also consider a model describing the coupling of a generic dilaton to the standard matter fields with five parameters, for a light field: We find that, for masses smaller than 10^{-12} eV, the constraints on the dilaton coupling parameters are improved by one order of magnitude compared to previous equivalence principle tests.