diff --git a/gnu/packages/base.scm b/gnu/packages/base.scm
index 502684ff40..422424cbe8 100644
--- a/gnu/packages/base.scm
+++ b/gnu/packages/base.scm
@@ -160,6 +160,13 @@ (define-public tar
                          (("/bin/sh")
                           (string-append bash "/bin/sh")))
                        #t))))))
+
+   ;; When cross-compiling, the 'set-shell-file-name' phase needs to be able
+   ;; to refer to the target Bash.
+   (inputs (if (%current-target-system)
+               `(("bash" ,bash))
+               '()))
+
    (synopsis "Managing tar archives")
    (description
     "Tar provides the ability to create tar archives, as well as the