Center of a circle and shopping center

They're two different meanings for the same word. From the Oxford Dictionary (which has "centre" rather than "center" but we can ignore that distinction, I think):

http://www.oxforddictionaries.com/definition/english/centre

1: The point that is equally distant from every point on the circumference of a circle or sphere.

2: The point from which an activity or process is directed, or on which it is focused

It doesn't make sense to say that a shopping centre is at the "middle" of the shopping - if anything, it's the other way round: the shopping is contained within the "shopping centre".

Center of a circle is the original meaning, by extension "the middle of anything" that is of the shopping in your specific case:

• late 14c., "middle point of a circle; point round which something revolves," from Old French centre (14c.), from Latin centrum "center," originally fixed point of the two points of a drafting compass, from Greek kentron "sharp point, goad, sting of a wasp," from kentein "stitch," from PIE root *kent- "to prick" (source also of Breton kentr "a spur," Welsh cethr "nail," Old High German hantag "sharp, pointed").

• Figuratively from 1680s. Meaning "the middle of anything" attested from 1590s. Spelling with -re popularized in Britain by Johnson's dictionary (following Bailey's), though -er is older and was used by Shakespeare, Milton, and Pope. Center of gravity is recorded from 1650s. Center of attention is from 1868.

(Etymonline)