Actually it dates back to ancient Greece. One of the earliest known link between owls and wisdom is their association with the Greek Goddess of Wisdom, Athena. She is often depicted holding an owl. Owls came to be associated with her because a particular species of owl was common on top of the Arcopolis of Athens. Since that hilltop was dedicated to Athena, the Greeks took the fact that there were so many Owls present as them being sacred to Athena. As a result the Owl and Athena have been linked and the Owl has come to represent Wisdom in many later cultures, heck right down to Owl in Winnie the Pooh...
In reality, they have very small brains and aren't wise at all.
The owl is both a strange looking and one that behaves quite differently from other birds. The result is that all kinds of legends have grown up about it. In the ancient time owl was known as unlucky bird in some country such as Roam. It was used to be caught in daylight and was burned. Its ashes were publicly scattered in the Tiber.
Yet in England and elsewhere it is often referred to as "the wise old owl". This is probably due to its appearance, not to any superior intelligence. Its staring eyes seem to be looking at as if the owl were thinking very hard. Actually, those eyes are very sensitive to daylight. They are so placed that the owl has to turn its whole head in order to change the direction of its glance.
Owls of one species or other are found in all parts of the world. The owl hunts only at night, but its eyes and ears are remarkable keen. In the ancient time the owl was the worship in Egypt and India. Still this custom can be seen in India.
Because it keeps its eyes open and (compared to other birds) its mouth shut.
The Biblical phrase "wise as a serpent" has the same connotation: Serpents keep their eyes open and their mouths shut.