diff --git a/kustomize.Dockerfile b/kustomize.Dockerfile
index 66f59ee926..48fab6b0bc 100644
--- a/kustomize.Dockerfile
+++ b/kustomize.Dockerfile
@@ -1,15 +1,16 @@
 # Copyright 2022 The Kubernetes Authors.
 # SPDX-License-Identifier: Apache-2.0
+ARG TARGETARCH TARGETOS
 
 # build
-FROM public.ecr.aws/docker/library/golang:1.22.7-bullseye as builder
+FROM --platform=${BUILDPLATFORM} public.ecr.aws/docker/library/golang:1.22.7-bullseye as builder
 ARG VERSION
 ARG COMMIT
 ARG DATE
 RUN mkdir /build
 ADD . /build/
 WORKDIR /build/kustomize
-RUN CGO_ENABLED=0 GO111MODULE=on go build \
+RUN CGO_ENABLED=0 GO111MODULE=on GOOS=${TARGETOS} GOARCH=${TARGETARCH} go build \
     -ldflags="-s -X sigs.k8s.io/kustomize/api/provenance.version=${VERSION} \
     -X sigs.k8s.io/kustomize/api/provenance.buildDate=${DATE}"
 
diff --git a/releasing/cloudbuild_kustomize_image.yaml b/releasing/cloudbuild_kustomize_image.yaml
index 605b292171..3aa325f54a 100644
--- a/releasing/cloudbuild_kustomize_image.yaml
+++ b/releasing/cloudbuild_kustomize_image.yaml
@@ -29,6 +29,8 @@ steps:
         COMMIT=$(git rev-parse HEAD)
         --build-arg
         DATE=$(date -u +%FT%TZ)
+        --platform
+        linux/amd64,linux/arm64
         .
 
 images: