1680s, "of or pertaining to the mind as a subject of study;" see psychology + -ical. In early 20c. the sense gradually shifted toward "affecting or pertaining to a person's mental or emotional state." Related: Psychologically. Psychological warfare "use of propaganda, etc., to undermine an enemy's morale or resolve" is recorded from 1940. Psychological moment was in vogue from 1871, from French moment psychologique "moment of immediate expectation of something about to happen."
The original German phrase, misinterpreted by the French & imported together with its false sense into English, meant the psychic factor, the mental effect, the influence exerted by a state of mind, & not a point of time at all, das Moment in German corresponding to our momentum, not our moment. [Fowler]