APL (and derivatives such as J) have boxing. J has two monadic operators
> called 'enclose'/'box', and 'disclose'/'unbox'. I'm not sure when it was introduced.
Usenet is often a good place to find things like this:
Here is a reference to boxing in Prolog from 1988.
Here is a reference to boxing in Lisp from 1984.
Everything prior to this points to Lisp as the origin of the term.
Performance and Evaluation of Lisp Systems (1985) discusses boxing.
(Interestingly, 'lisp boxing' is hard to search for, as apparently boxers (the people) often develop one.)
The TXDT Package - Interlisp Text Editing Primitives (1981) mentions it.
CSL 76-5, The Interlisp Virtual Machine specification (1976) uses it liberally.
The BBN-LISP system (1969) uses the term, but a previous document The BBN-LISP system (Feb 1966) doesn't. A document from later that year, Preliminary Specifications for BBN 940 LISP (Oct 1966) does.
I think that Basic PDP-1 Lisp (the predecessor of BBN Lisp) includes the required functions (see this book) to implement boxing/unboxing (LOC/VAG), but they don't appear to be used to do this.
Other Lisps (e.g. MacLisp) use similar techniques, but the word itself seems to have appeared somewhere in the Basic PDP-1 – BBN-Lisp – Interlisp lineage.