diff --git a/integration-cli/docker_cli_oom_killed_test.go b/integration-cli/docker_cli_oom_killed_test.go
deleted file mode 100644
index 54c34d206a..0000000000
--- a/integration-cli/docker_cli_oom_killed_test.go
+++ /dev/null
@@ -1,30 +0,0 @@
-// +build !windows
-
-package main
-
-import (
-	"github.com/docker/docker/integration-cli/checker"
-	"github.com/go-check/check"
-)
-
-func (s *DockerSuite) TestInspectOomKilledTrue(c *check.C) {
-	testRequires(c, DaemonIsLinux, memoryLimitSupport, swapMemorySupport)
-
-	name := "testoomkilled"
-	_, exitCode, _ := dockerCmdWithError("run", "--name", name, "--memory", "32MB", "busybox", "sh", "-c", "x=a; while true; do x=$x$x$x$x; done")
-
-	c.Assert(exitCode, checker.Equals, 137, check.Commentf("OOM exit should be 137"))
-
-	oomKilled := inspectField(c, name, "State.OOMKilled")
-	c.Assert(oomKilled, checker.Equals, "true")
-}
-
-func (s *DockerSuite) TestInspectOomKilledFalse(c *check.C) {
-	testRequires(c, DaemonIsLinux, memoryLimitSupport, swapMemorySupport)
-
-	name := "testoomkilled"
-	dockerCmd(c, "run", "--name", name, "--memory", "32MB", "busybox", "sh", "-c", "echo hello world")
-
-	oomKilled := inspectField(c, name, "State.OOMKilled")
-	c.Assert(oomKilled, checker.Equals, "false")
-}
diff --git a/integration/container/kill_test.go b/integration/container/kill_test.go
index 6efc5fc61d..d399213ac6 100644
--- a/integration/container/kill_test.go
+++ b/integration/container/kill_test.go
@@ -11,6 +11,7 @@ import (
 	"github.com/docker/docker/integration/internal/request"
 	"github.com/gotestyourself/gotestyourself/poll"
 	"github.com/gotestyourself/gotestyourself/skip"
+	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 )
 
@@ -146,3 +147,39 @@ func TestKillDifferentUserContainer(t *testing.T) {
 	require.NoError(t, err)
 	poll.WaitOn(t, containerIsInState(ctx, client, id, "exited"), poll.WithDelay(100*time.Millisecond))
 }
+
+func TestInspectOomKilledTrue(t *testing.T) {
+	skip.If(t, testEnv.DaemonInfo.OSType != "linux" || !testEnv.DaemonInfo.MemoryLimit || !testEnv.DaemonInfo.SwapLimit)
+
+	defer setupTest(t)()
+	ctx := context.Background()
+	client := request.NewAPIClient(t)
+
+	name := "testoomkilled"
+	cID := container.Run(t, ctx, client, container.WithName(name), container.WithCmd("sh", "-c", "x=a; while true; do x=$x$x$x$x; done"), func(c *container.TestContainerConfig) {
+		c.HostConfig.Resources.Memory = 32 * 1024 * 1024
+	})
+
+	poll.WaitOn(t, containerIsInState(ctx, client, cID, "exited"), poll.WithDelay(100*time.Millisecond))
+
+	inspect, err := client.ContainerInspect(ctx, cID)
+	require.NoError(t, err)
+	assert.Equal(t, inspect.State.OOMKilled, true)
+}
+
+func TestInspectOomKilledFalse(t *testing.T) {
+	skip.If(t, testEnv.DaemonInfo.OSType != "linux" || !testEnv.DaemonInfo.MemoryLimit || !testEnv.DaemonInfo.SwapLimit)
+
+	defer setupTest(t)()
+	ctx := context.Background()
+	client := request.NewAPIClient(t)
+
+	name := "testoomkilled"
+	cID := container.Run(t, ctx, client, container.WithName(name), container.WithCmd("sh", "-c", "echo hello world"))
+
+	poll.WaitOn(t, containerIsInState(ctx, client, cID, "exited"), poll.WithDelay(100*time.Millisecond))
+
+	inspect, err := client.ContainerInspect(ctx, cID)
+	require.NoError(t, err)
+	assert.Equal(t, inspect.State.OOMKilled, false)
+}