diff --git a/src/io/io.go b/src/io/io.go
index 4e49a782dce..cb2a37e4270 100644
--- a/src/io/io.go
+++ b/src/io/io.go
@@ -479,7 +479,16 @@ func (l *LimitedReader) Read(p []byte) (n int, err error) {
 // NewSectionReader returns a SectionReader that reads from r
 // starting at offset off and stops with EOF after n bytes.
 func NewSectionReader(r ReaderAt, off int64, n int64) *SectionReader {
-	return &SectionReader{r, off, off, off + n}
+	var remaining int64
+	const maxint64 = 1<<63 - 1
+	if off <= maxint64-n {
+		remaining = n + off
+	} else {
+		// Overflow, with no way to return error.
+		// Assume we can read up to an offset of 1<<63 - 1.
+		remaining = maxint64
+	}
+	return &SectionReader{r, off, off, remaining}
 }
 
 // SectionReader implements Read, Seek, and ReadAt on a section
diff --git a/src/io/io_test.go b/src/io/io_test.go
index 5b355e8c55b..30884604809 100644
--- a/src/io/io_test.go
+++ b/src/io/io_test.go
@@ -430,6 +430,20 @@ func TestSectionReader_Size(t *testing.T) {
 	}
 }
 
+func TestSectionReader_Max(t *testing.T) {
+	r := strings.NewReader("abcdef")
+	const maxint64 = 1<<63 - 1
+	sr := NewSectionReader(r, 3, maxint64)
+	n, err := sr.Read(make([]byte, 3))
+	if n != 3 || err != nil {
+		t.Errorf("Read = %v %v, want 3, nil", n, err)
+	}
+	n, err = sr.Read(make([]byte, 3))
+	if n != 0 || err != EOF {
+		t.Errorf("Read = %v, %v, want 0, EOF", n, err)
+	}
+}
+
 // largeWriter returns an invalid count that is larger than the number
 // of bytes provided (issue 39978).
 type largeWriter struct {