The storm was 60 miles (100 km) south of the beach city of Zihuatanejo in Guerrero state as of 10 p.m. (0300 GMT), with "strong gusty winds and heavy rains" spreading.
Rick was packing maximum sustained winds of 90 miles (150 km) per hour as it edged northward at about 6 miles (9 km) per hour.
The NHC estimated the hurricane's center would reach land by late Monday morning, pummeling the coast from Tecpan de Galeana in Guerrero, just north of Acapulco, to Punta San Telmo in Michoacan state.
Rain in parts of Guerrero and Michoacan was expected to amount to 20 inches, likely causing flooding and mudslides, the NHC said.
Mexico's civil protection agency told residents in the southern parts of those states to stay indoors as of Sunday evening.