diff --git a/opts/opts.go b/opts/opts.go
index 0a7706ca71ff..ed1c2b8a92d6 100644
--- a/opts/opts.go
+++ b/opts/opts.go
@@ -366,6 +366,10 @@ func ParseCPUs(value string) (int64, error) {
 	if !nano.IsInt() {
 		return 0, errors.New("value is too precise")
 	}
+	// Int64 keeps the low 64 bits of a value that does not fit.
+	if !nano.Num().IsInt64() {
+		return 0, errors.New("value is out of range")
+	}
 	return nano.Num().Int64(), nil
 }
 
diff --git a/opts/opts_test.go b/opts/opts_test.go
index 598a54a90efa..78425b43417c 100644
--- a/opts/opts_test.go
+++ b/opts/opts_test.go
@@ -2,6 +2,7 @@ package opts
 
 import (
 	"fmt"
+	"math"
 	"strings"
 	"testing"
 
@@ -429,6 +430,28 @@ func TestParseCPUsReturnZeroOnInvalidValues(t *testing.T) {
 	assert.Equal(t, z1, resValue)
 }
 
+func TestParseCPUsRejectsValuesThatDoNotFitInInt64(t *testing.T) {
+	got, err := ParseCPUs("10000000000")
+	assert.Error(t, err, "value is out of range")
+	assert.Equal(t, int64(0), got)
+
+	got, err = ParseCPUs("9223372036.854775808")
+	assert.Error(t, err, "value is out of range")
+	assert.Equal(t, int64(0), got)
+
+	got, err = ParseCPUs("-9223372036.854775809")
+	assert.Error(t, err, "value is out of range")
+	assert.Equal(t, int64(0), got)
+
+	got, err = ParseCPUs("9223372036.854775807")
+	assert.NilError(t, err)
+	assert.Equal(t, int64(math.MaxInt64), got)
+
+	got, err = ParseCPUs("-9223372036.854775808")
+	assert.NilError(t, err)
+	assert.Equal(t, int64(math.MinInt64), got)
+}
+
 func TestUmaskOpt(t *testing.T) {
 	t.Run("type", func(t *testing.T) {
 		var opt UmaskOpt