We perform an indirect search for weakly interacting massive particles (WIM
Ps) using the MACRO detector to look for neutrino-induced upward-going muon
s resulting from the annihilation of WIMPs trapped in the Sun and Earth. Th
e search is conducted in various angular cones centered on the Sun and Eart
h to accommodate a range of WIMP masses. No significant excess over the bac
kground from atmospheric neutrinos is seen. We set experimental flux limits
on the upward-going muon fluxes the Sun and the Earth. These limits are us
ed to constrain neutralino particle parameters from supersymmetric theory,
including those suggested by recent results from DAMA-NaI. [S0556-2821(99)0
4118-1].