If you have docker you can do whatever you want really since you can pull and start any image. So if you want to build and deploy:

docker login
docker build foo/bar .
docker push
docker run -v ~/.kube:/root/.kube lachlanevenson/k8s-kubectl set image deploy bar app=foo/bar

put this in your Dockerfile

RUN curl -LO https://storage.googleapis.com/kubernetes-release/release/$(curl -s https://storage.googleapis.com/kubernetes-release/release/stable.txt)/bin/linux/amd64/kubectl
RUN chmod +x ./kubectl
RUN mv ./kubectl /usr/local/bin

You just need to map kubectl (e.g. /usr/local/bin/kubectl) binary file and kubeconfig (e.g. /root/.kube/config) into your container.

For example (yaml file for Deployment):

      containers:
      - image: container-image-name
        name: container-name
        volumeMounts:
        - name: kubectl-binary
          mountPath: /usr/local/bin/kubectl
          readOnly: true
        - name: kubectl-config
          mountPath: /root/.kube/config
          readOnly: true
      volumes:
      - name: kubectl-binary
        hostPath:
          path: /usr/local/bin/kubectl
      - name: kubectl-config
        hostPath:
          path: /root/.kube/config

P.S.

use the following command to download kubectl binary file on each node, and copy /root/.kube/config to each node:

$ curl -L https://dl.k8s.io/v1.10.6/bin/linux/amd64/kubectl -o /usr/local/bin/kubectl

Weike's solution works fine for me with different kubectl path, any how if some one looking for solution to install the kubectl in the Docker image then here is the Docker file (it also installs python and kubernetes python client api, if we want to access cluster through python client api):

FROM base_image

WORKDIR /tmp


RUN  /usr/bin/curl -LO https://storage.googleapis.com/kubernetes-release/release/$(curl -s https://storage.googleapis.com/kubernetes-release/release/stable.txt)/bin/linux/amd64/kubectl \
     && chmod +x ./kubectl  \
     &&  mv ./kubectl /usr/local/bin/kubectl \
     && zypper install -y python2 \
     && zypper install -y python2-pip \
     && pip install kubernetes \
     && zypper install -y git \
     && zypper clean -a \
     && git clone --recursive https://github.com/kubernetes-client/python.git \
     && cd python \
     && python setup.py install

Also here is my deployment file to map kubectl binary and configuration to container to access kubectl in the kubernetes container with in the pod:

apiVersion: apps/v1
kind: Deployment
metadata:
  name: support
  labels:
    app: support
  namespace: default
spec:
  replicas: 1
  selector:
    matchLabels:
      app: support
  template:
    metadata:
      labels:
        app: support
    spec:
      terminationGracePeriodSeconds: 3
      imagePullSecrets:
      - name: mysecret
      containers:
        - name: support
          image: image-name
          command:
            - "/bin/sh"
            - "-c"
            - "sleep infinity"
          volumeMounts:
          - name: kubectl-binary
            mountPath: /usr/bin/kubectl
            readOnly: true
          - name: kubectl-config
            mountPath: /etc/kubernetes/config
            readOnly: true
      volumes:
        - name: kubectl-binary
          hostPath:
            path: /usr/bin/kubectl
        - name: kubectl-config
          hostPath:
            path: /etc/kubernetes/config