diff --git a/share/spack/spack-completion.bash b/share/spack/spack-completion.bash
index 65d276b9743..04209c35dd2 100644
--- a/share/spack/spack-completion.bash
+++ b/share/spack/spack-completion.bash
@@ -1335,7 +1335,7 @@ _spack_info() {
 _spack_install() {
     if $list_options
     then
-        SPACK_COMPREPLY="-h --help --only -u --until -j --jobs --overwrite --fail-fast --keep-prefix --keep-stage --dont-restage --use-cache --no-cache --cache-only --use-buildcache --include-build-deps --no-check-signature --show-log-on-error --source -n --no-checksum -v --verbose --fake --only-concrete --add --no-add -f --file --clean --dirty --test --log-format --log-file --help-cdash --cdash-upload-url --cdash-build --cdash-site --cdash-track --cdash-buildstamp -y --yes-to-all -U --fresh --reuse --fresh-roots --reuse-deps --deprecated"
+        SPACK_COMPREPLY="-h --help --only -u --until -p --concurrent-packages -j --jobs --overwrite --fail-fast --keep-prefix --keep-stage --dont-restage --use-cache --no-cache --cache-only --use-buildcache --include-build-deps --no-check-signature --show-log-on-error --source -n --no-checksum -v --verbose --fake --only-concrete --add --no-add -f --file --clean --dirty --test --log-format --log-file --help-cdash --cdash-upload-url --cdash-build --cdash-site --cdash-track --cdash-buildstamp -y --yes-to-all -U --fresh --reuse --fresh-roots --reuse-deps --deprecated"
     else
         _all_packages
     fi
diff --git a/share/spack/spack-completion.fish b/share/spack/spack-completion.fish
index 0a6c986757f..954a130ad43 100644
--- a/share/spack/spack-completion.fish
+++ b/share/spack/spack-completion.fish
@@ -2025,7 +2025,7 @@ complete -c spack -n '__fish_spack_using_command info' -l variants-by-name -f -a
 complete -c spack -n '__fish_spack_using_command info' -l variants-by-name -d 'list variants in strict name order; don'"'"'t group by condition'
 
 # spack install
-set -g __fish_spack_optspecs_spack_install h/help only= u/until= j/jobs= overwrite fail-fast keep-prefix keep-stage dont-restage use-cache no-cache cache-only use-buildcache= include-build-deps no-check-signature show-log-on-error source n/no-checksum v/verbose fake only-concrete add no-add f/file= clean dirty test= log-format= log-file= help-cdash cdash-upload-url= cdash-build= cdash-site= cdash-track= cdash-buildstamp= y/yes-to-all U/fresh reuse fresh-roots deprecated
+set -g __fish_spack_optspecs_spack_install h/help only= u/until= p/concurrent-packages= j/jobs= overwrite fail-fast keep-prefix keep-stage dont-restage use-cache no-cache cache-only use-buildcache= include-build-deps no-check-signature show-log-on-error source n/no-checksum v/verbose fake only-concrete add no-add f/file= clean dirty test= log-format= log-file= help-cdash cdash-upload-url= cdash-build= cdash-site= cdash-track= cdash-buildstamp= y/yes-to-all U/fresh reuse fresh-roots deprecated
 complete -c spack -n '__fish_spack_using_command_pos_remainder 0 install' -f -k -a '(__fish_spack_specs)'
 complete -c spack -n '__fish_spack_using_command install' -s h -l help -f -a help
 complete -c spack -n '__fish_spack_using_command install' -s h -l help -d 'show this help message and exit'
@@ -2033,6 +2033,8 @@ complete -c spack -n '__fish_spack_using_command install' -l only -r -f -a 'pack
 complete -c spack -n '__fish_spack_using_command install' -l only -r -d 'select the mode of installation'
 complete -c spack -n '__fish_spack_using_command install' -s u -l until -r -f -a until
 complete -c spack -n '__fish_spack_using_command install' -s u -l until -r -d 'phase to stop after when installing (default None)'
+complete -c spack -n '__fish_spack_using_command install' -s p -l concurrent-packages -r -f -a concurrent_packages
+complete -c spack -n '__fish_spack_using_command install' -s p -l concurrent-packages -r -d 'maximum number of packages to build concurrently'
 complete -c spack -n '__fish_spack_using_command install' -s j -l jobs -r -f -a jobs
 complete -c spack -n '__fish_spack_using_command install' -s j -l jobs -r -d 'explicitly set number of parallel jobs'
 complete -c spack -n '__fish_spack_using_command install' -l overwrite -f -a overwrite