Here's one hack.

#lang racket/base

(require
  math/array
 (prefix-in rkt: racket/serialize))

(define secret-key 'array)

(define (serialize val)
  (if (array? val)
    (rkt:serialize (cons secret-key (array->list val)))
    (rkt:serialize val)))

(define (deserialize val)
  (define d (rkt:deserialize val))
  (if (and (pair? d) (eq? secret-key (car d)))
    (list->array (cdr d))
    d))

(define arr (array #[0 1 2]))
(serialize arr)
(deserialize (serialize arr))

(Part of the issue serializing math/array is that it represents arrays as
functions under the hood)

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