Google seems not to be providing any results. Therefore, I believe the origin of this quotation is unknown.
It appears to have entered the public consciousness as a common expression and exists in many different forms, varying slightly depending on who says or writes about it. For example, "God has His flies even if he needs bigger spiders for them" and "Even God must use spider webs to capture its fruit flies" are two variations.
This phrase may be related to an old proverb popularized by Benjamin Franklin that reads: "For want of a nail, the shoe was lost; for want of a shoe, the horse was lost; and for want of a horse, the rider was lost," exemplifying how small lapses can cause large consequences—a message echoed by imagery present when comparing god-sized fruitflies with god-sized spiders necessary to trap them.