diff --git a/CHANGELOG.md b/CHANGELOG.md
index 946b6ae7c..6cb6790f7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -15,3 +15,4 @@
 * [ENHANCEMENT] Replace go-kit/kit/log with go-kit/log. #52
 * [ENHANCEMENT] Add spanlogger package. #42
 * [BUGFIX] spanlogger: Support multiple tenant IDs. #59
+* [ENHANCEMENT] Add runutil.CloseWithLogOnErr function. #58
diff --git a/go.mod b/go.mod
index 29381a69e..b2daf3722 100644
--- a/go.mod
+++ b/go.mod
@@ -9,6 +9,7 @@ require (
 	github.com/gogo/protobuf v1.3.2
 	github.com/gogo/status v1.1.0
 	github.com/golang/snappy v0.0.4
+	github.com/google/go-cmp v0.5.5
 	github.com/gorilla/mux v1.8.0 // indirect
 	github.com/grpc-ecosystem/go-grpc-middleware v1.1.0
 	github.com/hashicorp/consul/api v1.9.1
diff --git a/runutil/capture.go b/runutil/capture.go
deleted file mode 100644
index 4e17b9c06..000000000
--- a/runutil/capture.go
+++ /dev/null
@@ -1,15 +0,0 @@
-package runutil
-
-import (
-	"io"
-
-	"github.com/pkg/errors"
-
-	"github.com/grafana/dskit/multierror"
-)
-
-// CloseWithErrCapture closes closer and wraps any error with the provided message and assigns it to err.
-func CloseWithErrCapture(err *error, closer io.Closer, msg string) {
-	merr := multierror.New(*err, errors.Wrap(closer.Close(), msg))
-	*err = merr.Err()
-}
diff --git a/runutil/runutil.go b/runutil/runutil.go
new file mode 100644
index 000000000..bea0e3e4b
--- /dev/null
+++ b/runutil/runutil.go
@@ -0,0 +1,31 @@
+package runutil
+
+import (
+	"fmt"
+	"io"
+	"os"
+
+	"github.com/go-kit/log"
+	"github.com/go-kit/log/level"
+	"github.com/pkg/errors"
+
+	"github.com/grafana/dskit/multierror"
+)
+
+// CloseWithErrCapture closes closer and wraps any error with the provided message and assigns it to err.
+func CloseWithErrCapture(err *error, closer io.Closer, msg string) {
+	merr := multierror.New(*err, errors.Wrap(closer.Close(), msg))
+	*err = merr.Err()
+}
+
+// CloseWithLogOnErr closes an io.Closer and logs any relevant error from it wrapped with the provided format string and
+// args.
+func CloseWithLogOnErr(logger log.Logger, closer io.Closer, format string, args ...interface{}) {
+	err := closer.Close()
+	if err == nil || errors.Is(err, os.ErrClosed) {
+		return
+	}
+
+	msg := fmt.Sprintf(format, args...)
+	level.Warn(logger).Log("msg", "detected close error", "err", fmt.Sprintf("%s: %s", msg, err.Error()))
+}
diff --git a/runutil/runutil_test.go b/runutil/runutil_test.go
new file mode 100644
index 000000000..b0d35ac00
--- /dev/null
+++ b/runutil/runutil_test.go
@@ -0,0 +1,62 @@
+package runutil
+
+import (
+	"fmt"
+	"os"
+	"testing"
+
+	"github.com/go-kit/log/level"
+	"github.com/google/go-cmp/cmp"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestCloseWithLogOnErr(t *testing.T) {
+	t.Run("With non-close error", func(t *testing.T) {
+		closer := fakeCloser{err: fmt.Errorf("an error")}
+		logger := fakeLogger{}
+
+		CloseWithLogOnErr(&logger, closer, "closing failed")
+
+		assert.Empty(t, cmp.Diff([]interface{}{
+			"level", level.WarnValue(), "msg", "detected close error", "err", "closing failed: an error",
+		}, logger.keyvals, cmp.Comparer(func(a, b fmt.Stringer) bool {
+			t.Logf("Comparing %q and %q", a.String(), b.String())
+			return a.String() == b.String()
+		})))
+	})
+
+	t.Run("With no error", func(t *testing.T) {
+		closer := fakeCloser{}
+		logger := fakeLogger{}
+
+		CloseWithLogOnErr(&logger, closer, "closing failed")
+
+		assert.Empty(t, logger.keyvals)
+	})
+
+	t.Run("With closed error", func(t *testing.T) {
+		closer := fakeCloser{err: os.ErrClosed}
+		logger := fakeLogger{}
+
+		CloseWithLogOnErr(&logger, closer, "closing failed")
+
+		assert.Empty(t, logger.keyvals)
+	})
+}
+
+type fakeCloser struct {
+	err error
+}
+
+func (c fakeCloser) Close() error {
+	return c.err
+}
+
+type fakeLogger struct {
+	keyvals []interface{}
+}
+
+func (l *fakeLogger) Log(keyvals ...interface{}) error {
+	l.keyvals = keyvals
+	return nil
+}