Catalyzes the reversible phosphorylation of S-methyl-5'-thioinosine (MTI) to hypoxanthine and 5-methylthioribose-1-phosphate. Involved in the breakdown of S-methyl-5'-thioadenosine (MTA), a major by-product of polyamine biosynthesis. Catabolism of (MTA) occurs via deamination to MTI and phosphorolysis to hypoxanthine (By similarity).