Catalyzes the phosphorylation of methylthioribose into methylthioribose-1-phosphate. 5-(methylsulfanyl)-D-ribose + ATP = ADP + H(+) + S-methyl-5-thio-alpha-D-ribose 1-phosphate Amino-acid biosynthesis; L-methionine biosynthesis via salvage pathway; S-methyl-5-thio-alpha-D-ribose 1-phosphate from S-methyl-5'-thioadenosine (hydrolase route): step 2/2. Homodimer. Belongs to the methylthioribose kinase family.