Kartik Ayyar, Machine Learning Engineer at Google:

The word shrink seems to be slang for "headshrinker". Its first recorded use was in Thomas Pynchon's book "The Crying of Lot 49 published" in 1966.

"Shrink" likely originated from a commingling of the two words "head shrink" and the single word "headshrinker," indicating that it likely originated as a disparaging reference comparing the process of psychotherapy to primitive tribal practices of shrinking the heads of enemies.

 The idea being that a shrink tries to get into your head in a manner similar to how someone trying to shrink your head would.