Irreversible Origami Envelope
While not impossible to open without tearing, and requiring cuts as well as folds (which disqualifies the method as origami to an origami purist), there is a form of letterlocking that involves cutting a thin strip from the blank margin of the letter, folding the letter, and then punching holes through the letter with an awl, and threading the strip through the holes in an interlocking knot-like pattern, which would make it very difficult to open the letter without tearing the thin delicate strip of paper.

See: https://vimeo.com/189348055

http://letterlocking.org/categories states that this blank margin method of letterlocking was "used by Queen Elizabeth I of England, Mary Queen of Scots, Catherine DeMedici, and many others."