“Profite” is definitely wrong because it doesn't have to be detrimental. There can be mutual profit, but exploitation is one-sided. There isn't any significant difference between English and French here.
System” should be “système”.
“Les moins riches” is not quite right: it encompasses more people than “poorest”. A straightforward translation “les plus pauvres” would be more accurate. However, the word pauvre is slightly pejorative (or maybe guilt-inducing) in late 20th/early 21st century French. Other adjectives such as démuni (which tends to apply to individual people) or défavorisé (which tends to apply to communities) are more common.
Ce système créé par le gouvernement exploite les communautés les plus défavorisées.