diff --git a/daemon/logger/loggerutils/logfile.go b/daemon/logger/loggerutils/logfile.go
index ff7a3323f9..a9d9d633db 100644
--- a/daemon/logger/loggerutils/logfile.go
+++ b/daemon/logger/loggerutils/logfile.go
@@ -192,8 +192,12 @@ func (w *LogFile) ReadLogs(config logger.ReadConfig, watcher *logger.LogWatcher)
 		for _, f := range files {
 			seekers = append(seekers, f)
 		}
-		seekers = append(seekers, currentChunk)
-		tailFile(multireader.MultiReadSeeker(seekers...), watcher, w.createDecoder, config)
+		if currentChunk.Size() > 0 {
+			seekers = append(seekers, currentChunk)
+		}
+		if len(seekers) > 0 {
+			tailFile(multireader.MultiReadSeeker(seekers...), watcher, w.createDecoder, config)
+		}
 	}
 
 	w.mu.RLock()
diff --git a/integration/container/logs_test.go b/integration/container/logs_test.go
new file mode 100644
index 0000000000..1157da14b8
--- /dev/null
+++ b/integration/container/logs_test.go
@@ -0,0 +1,33 @@
+package container
+
+import (
+	"context"
+	"io/ioutil"
+	"testing"
+
+	"github.com/docker/docker/api/types"
+	"github.com/docker/docker/integration/internal/container"
+	"github.com/docker/docker/integration/internal/request"
+	"github.com/docker/docker/pkg/stdcopy"
+	"github.com/stretchr/testify/assert"
+)
+
+// Regression test for #35370
+// Makes sure that when following we don't get an EOF error when there are no logs
+func TestLogsFollowTailEmpty(t *testing.T) {
+	defer setupTest(t)()
+	client := request.NewAPIClient(t)
+	ctx := context.Background()
+
+	id := container.Run(t, ctx, client, container.WithCmd("sleep", "100000"))
+	defer client.ContainerRemove(ctx, id, types.ContainerRemoveOptions{Force: true})
+
+	logs, err := client.ContainerLogs(ctx, id, types.ContainerLogsOptions{ShowStdout: true, Tail: "2"})
+	if logs != nil {
+		defer logs.Close()
+	}
+	assert.NoError(t, err)
+
+	_, err = stdcopy.StdCopy(ioutil.Discard, ioutil.Discard, logs)
+	assert.NoError(t, err)
+}