diff --git a/integration-cli/docker_cli_run_unix_test.go b/integration-cli/docker_cli_run_unix_test.go
index 13576c760d..6392f935d9 100644
--- a/integration-cli/docker_cli_run_unix_test.go
+++ b/integration-cli/docker_cli_run_unix_test.go
@@ -497,7 +497,7 @@ func (s *DockerSuite) TestRunWithInvalidCpuPeriod(c *check.C) {
 }
 
 func (s *DockerSuite) TestRunWithKernelMemory(c *check.C) {
-	testRequires(c, kernelMemorySupport)
+	testRequires(c, DaemonIsLinux, kernelMemorySupport)
 
 	file := "/sys/fs/cgroup/memory/memory.kmem.limit_in_bytes"
 	cli.DockerCmd(c, "run", "--kernel-memory", "50M", "--name", "test1", "busybox", "cat", file).Assert(c, icmd.Expected{
@@ -510,7 +510,7 @@ func (s *DockerSuite) TestRunWithKernelMemory(c *check.C) {
 }
 
 func (s *DockerSuite) TestRunWithInvalidKernelMemory(c *check.C) {
-	testRequires(c, kernelMemorySupport)
+	testRequires(c, DaemonIsLinux, kernelMemorySupport)
 
 	out, _, err := dockerCmdWithError("run", "--kernel-memory", "2M", "busybox", "true")
 	c.Assert(err, check.NotNil)
diff --git a/integration-cli/requirements_unix_test.go b/integration-cli/requirements_unix_test.go
index f28e837f6d..cea1db1e6d 100644
--- a/integration-cli/requirements_unix_test.go
+++ b/integration-cli/requirements_unix_test.go
@@ -38,6 +38,17 @@ func pidsLimit() bool {
 }
 
 func kernelMemorySupport() bool {
+	// TODO remove this once kmem support in RHEL kernels is fixed. See https://github.com/opencontainers/runc/pull/1921
+	daemonV, err := kernel.ParseRelease(testEnv.DaemonInfo.KernelVersion)
+	if err != nil {
+		return false
+	}
+	requiredV := kernel.VersionInfo{Kernel: 3, Major: 10}
+	if kernel.CompareKernelVersion(*daemonV, requiredV) < 1 {
+		// On Kernel 3.10 and under, don't consider kernel memory to be supported,
+		// even if the kernel (and thus the daemon) reports it as being supported
+		return false
+	}
 	return testEnv.DaemonInfo.KernelMemory
 }
 
diff --git a/pkg/parsers/kernel/kernel_unix_test.go b/pkg/parsers/kernel/kernel_unix_test.go
index 2f36490c53..9d2e496af5 100644
--- a/pkg/parsers/kernel/kernel_unix_test.go
+++ b/pkg/parsers/kernel/kernel_unix_test.go
@@ -27,6 +27,7 @@ func TestParseRelease(t *testing.T) {
 	assertParseRelease(t, "3.4.54.longterm-1", &VersionInfo{Kernel: 3, Major: 4, Minor: 54, Flavor: ".longterm-1"}, 0)
 	assertParseRelease(t, "3.4.54.longterm-1", &VersionInfo{Kernel: 3, Major: 4, Minor: 54, Flavor: ".longterm-1"}, 0)
 	assertParseRelease(t, "3.8.0-19-generic", &VersionInfo{Kernel: 3, Major: 8, Minor: 0, Flavor: "-19-generic"}, 0)
+	assertParseRelease(t, "3.10.0-862.2.3.el7.x86_64", &VersionInfo{Kernel: 3, Major: 10, Minor: 0, Flavor: "-862.2.3.el7.x86_64"}, 0)
 	assertParseRelease(t, "3.12.8tag", &VersionInfo{Kernel: 3, Major: 12, Minor: 8, Flavor: "tag"}, 0)
 	assertParseRelease(t, "3.12-1-amd64", &VersionInfo{Kernel: 3, Major: 12, Minor: 0, Flavor: "-1-amd64"}, 0)
 	assertParseRelease(t, "3.8.0", &VersionInfo{Kernel: 4, Major: 8, Minor: 0}, -1)