diff --git a/daemon/kill.go b/daemon/kill.go
index 3e6457e9522dd..f3ac070337857 100644
--- a/daemon/kill.go
+++ b/daemon/kill.go
@@ -64,8 +64,6 @@ func (daemon *Daemon) killWithSignal(container *containerpkg.Container, sig int)
 	container.Lock()
 	defer container.Unlock()
 
-	daemon.stopHealthchecks(container)
-
 	if !container.Running {
 		return errNotRunning(container.ID)
 	}
diff --git a/integration/container/health_test.go b/integration/container/health_test.go
index f4117f562adcd..64284c8860426 100644
--- a/integration/container/health_test.go
+++ b/integration/container/health_test.go
@@ -9,6 +9,7 @@ import (
 	containertypes "github.com/docker/docker/api/types/container"
 	"github.com/docker/docker/client"
 	"github.com/docker/docker/integration/internal/container"
+	"gotest.tools/assert"
 	"gotest.tools/poll"
 	"gotest.tools/skip"
 )
@@ -32,6 +33,35 @@ func TestHealthCheckWorkdir(t *testing.T) {
 	poll.WaitOn(t, pollForHealthStatus(ctx, client, cID, types.Healthy), poll.WithDelay(100*time.Millisecond))
 }
 
+// GitHub #37263
+// Do not stop healthchecks just because we sent a signal to the container
+func TestHealthKillContainer(t *testing.T) {
+	skip.If(t, testEnv.OSType == "windows", "Windows only supports SIGKILL and SIGTERM? See https://github.com/moby/moby/issues/39574")
+	defer setupTest(t)()
+
+	ctx := context.Background()
+	client := testEnv.APIClient()
+
+	id := container.Run(t, ctx, client, func(c *container.TestContainerConfig) {
+		c.Config.Healthcheck = &containertypes.HealthConfig{
+			Test:     []string{"CMD-SHELL", "sleep 1"},
+			Interval: time.Second,
+			Retries:  5,
+		}
+	})
+
+	ctxPoll, cancel := context.WithTimeout(ctx, 30*time.Second)
+	defer cancel()
+	poll.WaitOn(t, pollForHealthStatus(ctxPoll, client, id, "healthy"), poll.WithDelay(100*time.Millisecond))
+
+	err := client.ContainerKill(ctx, id, "SIGUSR1")
+	assert.NilError(t, err)
+
+	ctxPoll, cancel = context.WithTimeout(ctx, 30*time.Second)
+	defer cancel()
+	poll.WaitOn(t, pollForHealthStatus(ctxPoll, client, id, "healthy"), poll.WithDelay(100*time.Millisecond))
+}
+
 func pollForHealthStatus(ctx context.Context, client client.APIClient, containerID string, healthStatus string) func(log poll.LogT) poll.Result {
 	return func(log poll.LogT) poll.Result {
 		inspect, err := client.ContainerInspect(ctx, containerID)