To my knowledge, the only FDA approved MMP inhibitor is the antibiotic doxycycline, approved under the name Periostat for severe periodontitis. It works on MMP-2, not the MMP-1,3, and 9 active in skin photoaging.
All the major pharmaceutical companies had active MMP inhibitor prospects targetted towards arthritis, osteoporosis, cancer, atherosclerosis, heart failure around the turn of the millenium, but dismal trial results ended that era. Most of the literature seems to date from 1996-2002.
For the most part, practical systemic reductions in MMP activity will come largely through anti-inflammatory measures, in particular inhibiting the signalling chain involving NF-kB and NADPH oxidase upstream of AP-1 and MMP expression.
Cox inhibitors (like aspirin and other NSAIDs), long-chain omega-6 fatty acids (EPA, fish oil), and food polyphenols all have a place here. Eg, the common berry/wine anthocyanidin delphidin inhibits MMP expression in vitro.