diff --git a/changelogs/unreleased/remove-redis-3-references.yml b/changelogs/unreleased/remove-redis-3-references.yml
new file mode 100644
index 0000000000000000000000000000000000000000..a7efb3ce17cd936e131e7f393d9ab41010d17584
--- /dev/null
+++ b/changelogs/unreleased/remove-redis-3-references.yml
@@ -0,0 +1,6 @@
+---
+title: Set minimum Redis version to 4 and recommended version to 5 in Redis check
+  task
+merge_request: 38475
+author:
+type: changed
diff --git a/doc/administration/raketasks/maintenance.md b/doc/administration/raketasks/maintenance.md
index 19781b6a5db557da8f469ef2c69afc88848efef4..553afba78e343bb819b6f4983593b1805e2fead0 100644
--- a/doc/administration/raketasks/maintenance.md
+++ b/doc/administration/raketasks/maintenance.md
@@ -23,32 +23,39 @@ Example output:
 
 ```plaintext
 System information
-System:           Debian 7.8
-Current User:     git
-Using RVM:        no
-Ruby Version:     2.1.5p273
-Gem Version:      2.4.3
-Bundler Version:  1.7.6
-Rake Version:     10.3.2
-Redis Version:    3.2.5
-Sidekiq Version:  2.17.8
+System:         Ubuntu 20.04
+Proxy:          no
+Current User:   git
+Using RVM:      no
+Ruby Version:   2.6.6p146
+Gem Version:    2.7.10
+Bundler Version:1.17.3
+Rake Version:   12.3.3
+Redis Version:  5.0.9
+Git Version:    2.27.0
+Sidekiq Version:5.2.9
+Go Version:     unknown
 
 GitLab information
-Version:          7.7.1
-Revision:         41ab9e1
-Directory:        /home/git/gitlab
-DB Adapter:       postgresql
-URL:              https://gitlab.example.com
-HTTP Clone URL:   https://gitlab.example.com/some-project.git
-SSH Clone URL:    git@gitlab.example.com:some-project.git
-Using LDAP:       no
-Using Omniauth:   no
+Version:        13.2.2-ee
+Revision:       618883a1f9d
+Directory:      /opt/gitlab/embedded/service/gitlab-rails
+DB Adapter:     PostgreSQL
+DB Version:     11.7
+URL:            http://gitlab.example.com
+HTTP Clone URL: http://gitlab.example.com/some-group/some-project.git
+SSH Clone URL:  git@gitlab.example.com:some-group/some-project.git
+Elasticsearch:  no
+Geo:            no
+Using LDAP:     no
+Using Omniauth: yes
+Omniauth Providers:
 
 GitLab Shell
-Version:          2.4.1
-Repositories:     /home/git/repositories/
-Hooks:            /home/git/gitlab-shell/hooks/
-Git:              /usr/bin/git
+Version:    13.3.0
+Repository storage paths:
+- default:  /var/opt/gitlab/git-data/repositories
+GitLab Shell path:      /opt/gitlab/embedded/service/gitlab-shell
 ```
 
 ## Show GitLab license information **(STARTER ONLY)**
diff --git a/doc/administration/redis/replication_and_failover_external.md b/doc/administration/redis/replication_and_failover_external.md
index d22a6ddea6f79e4397afe49c29ce88c3dc21b528..d530e6a8fd7c7f8ed431773e5b5ef2c1f356d1c8 100644
--- a/doc/administration/redis/replication_and_failover_external.md
+++ b/doc/administration/redis/replication_and_failover_external.md
@@ -19,13 +19,7 @@ The following are the requirements for providing your own Redis instance:
 
 - Redis version 5.0 or higher is recommended, as this is what ships with
   Omnibus GitLab packages starting with GitLab 12.7.
-- Support for Redis 3.2 is deprecated with GitLab 12.10 and will be completely
-  removed in GitLab 13.0.
-- GitLab 12.0 and later requires Redis version 3.2 or higher. Older Redis
-  versions do not support an optional count argument to SPOP which is now
-  required for [Merge Trains](../../ci/merge_request_pipelines/pipelines_for_merged_results/merge_trains/index.md).
-- In addition, if Redis 4 or later is available, GitLab makes use of certain
-  commands like `UNLINK` and `USAGE` which were introduced only in Redis 4.
+- GitLab 13.0 and later requires Redis version 4.0 or higher.
 - Standalone Redis or Redis high availability with Sentinel are supported. Redis
   Cluster is not supported.
 - Managed Redis from cloud providers such as AWS ElastiCache will work. If these
diff --git a/lib/system_check/app/redis_version_check.rb b/lib/system_check/app/redis_version_check.rb
index aca2972f2871edf7f25947249a0d0b7a8fc1c713..aff0ee52e0d05be1b117a3dc024709851b9db24e 100644
--- a/lib/system_check/app/redis_version_check.rb
+++ b/lib/system_check/app/redis_version_check.rb
@@ -5,8 +5,8 @@
 module SystemCheck
   module App
     class RedisVersionCheck < SystemCheck::BaseCheck
-      MIN_REDIS_VERSION = '3.2.0'
-      RECOMMENDED_REDIS_VERSION = '4.0.0'
+      MIN_REDIS_VERSION = '4.0.0'
+      RECOMMENDED_REDIS_VERSION = '4.0.0' # In future we may deprecate but still support Redis 4
       set_name "Redis version >= #{RECOMMENDED_REDIS_VERSION}?"
 
       @custom_error_message = ''