diff --git a/CHANGELOG.md b/CHANGELOG.md
index a8f4457749f..5afc3f4eab8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -25,6 +25,7 @@ NOTE: Add new changes BELOW THIS COMMENT.
 
 ### Added
 
+- Docker container's healthcheck ([#3290]).
 - Two new HTTP APIs, `PUT /control/stats/config/update` and `GET
   control/stats/config`, which can be used to set and receive the query log
   configuration.  See openapi/openapi.yaml for the full description.
@@ -123,6 +124,7 @@ In this release, the schema version has changed from 17 to 20.
 
 [#1163]: https://github.com/AdguardTeam/AdGuardHome/issues/1163
 [#1472]: https://github.com/AdguardTeam/AdGuardHome/issues/1472
+[#3290]: https://github.com/AdguardTeam/AdGuardHome/issues/3290
 [#5567]: https://github.com/AdguardTeam/AdGuardHome/issues/5567
 [#5584]: https://github.com/AdguardTeam/AdGuardHome/issues/5584
 
diff --git a/scripts/make/Dockerfile b/docker/Dockerfile
similarity index 97%
rename from scripts/make/Dockerfile
rename to docker/Dockerfile
index 2a87458e06c..38a34bcddfd 100644
--- a/scripts/make/Dockerfile
+++ b/docker/Dockerfile
@@ -52,7 +52,7 @@ RUN setcap 'cap_net_bind_service=+eip' /opt/adguardhome/AdGuardHome
 # TODO(a.garipov): Remove the old, non-standard 784 and 8853 ports for
 # DNS-over-QUIC in a future release.
 EXPOSE 53/tcp 53/udp 67/udp 68/udp 80/tcp 443/tcp 443/udp 784/udp\
-	853/tcp 853/udp 3000/tcp 3000/udp 3001/tcp 3001/udp 5443/tcp\
+	853/tcp 853/udp 3000/tcp 3000/udp 5443/tcp\
 	5443/udp 6060/tcp 8853/udp
 
 WORKDIR /opt/adguardhome/work
diff --git a/scripts/make/build-docker.sh b/scripts/make/build-docker.sh
index 270ba3128b7..7a6a055479d 100644
--- a/scripts/make/build-docker.sh
+++ b/scripts/make/build-docker.sh
@@ -87,7 +87,7 @@ readonly docker_image_full_name docker_tags
 
 # Copy the binaries into a new directory under new names, so that it's easier to
 # COPY them later.  DO NOT remove the trailing underscores.  See file
-# scripts/make/Dockerfile.
+# docker/Dockerfile.
 dist_docker="${dist_dir}/docker"
 readonly dist_docker
 
@@ -105,9 +105,18 @@ cp "${dist_dir}/AdGuardHome_linux_arm_7/AdGuardHome/AdGuardHome"\
 cp "${dist_dir}/AdGuardHome_linux_ppc64le/AdGuardHome/AdGuardHome"\
 	"${dist_docker}/AdGuardHome_linux_ppc64le_"
 
-# TODO(e.burkov):  !! do better
-cp -R "./docker"\
-	"${dist_docker}/scripts"
+# Copy the helper scripts.  DO NOT remove the trailing underscores.  See file
+# docker/Dockerfile.
+dist_docker_scripts="${dist_docker}/scripts"
+readonly dist_docker_scripts
+
+mkdir -p "$dist_docker_scripts"
+cp "./docker/dns-bind.awk"\
+	"${dist_docker}/scripts/dns-bind.awk"
+cp "./docker/web-bind.awk"\
+	"${dist_docker}/scripts/web-bind.awk"
+cp "./docker/healthcheck.sh"\
+	"${dist_docker}/scripts/healthcheck.sh"
 
 # Don't use quotes with $docker_tags and $debug_flags because we want word
 # splitting and or an empty space if tags are empty.
@@ -122,5 +131,5 @@ $sudo_cmd docker\
 	--platform "$docker_platforms"\
 	$docker_tags\
 	-t "$docker_image_full_name"\
-	-f ./scripts/make/Dockerfile\
+	-f ./docker/Dockerfile\
 	.