diff --git a/src/cmd/go/internal/work/exec.go b/src/cmd/go/internal/work/exec.go
index ecad324886..e05471b06c 100644
--- a/src/cmd/go/internal/work/exec.go
+++ b/src/cmd/go/internal/work/exec.go
@@ -629,19 +629,6 @@ OverlayLoop:
 		}
 	}
 
-	// Run SWIG on each .swig and .swigcxx file.
-	// Each run will generate two files, a .go file and a .c or .cxx file.
-	// The .go file will use import "C" and is to be processed by cgo.
-	if p.UsesSwig() {
-		outGo, outC, outCXX, err := b.swig(a, objdir, pcCFLAGS)
-		if err != nil {
-			return err
-		}
-		cgofiles = append(cgofiles, outGo...)
-		cfiles = append(cfiles, outC...)
-		cxxfiles = append(cxxfiles, outCXX...)
-	}
-
 	// If we're doing coverage, preprocess the .go files and put them in the work directory
 	if p.Internal.Cover.Mode != "" {
 		outfiles := []string{}
@@ -722,6 +709,22 @@ OverlayLoop:
 		}
 	}
 
+	// Run SWIG on each .swig and .swigcxx file.
+	// Each run will generate two files, a .go file and a .c or .cxx file.
+	// The .go file will use import "C" and is to be processed by cgo.
+	// For -cover test or build runs, this needs to happen after the cover
+	// tool is run; we don't want to instrument swig-generated Go files,
+	// see issue #64661.
+	if p.UsesSwig() {
+		outGo, outC, outCXX, err := b.swig(a, objdir, pcCFLAGS)
+		if err != nil {
+			return err
+		}
+		cgofiles = append(cgofiles, outGo...)
+		cfiles = append(cfiles, outC...)
+		cxxfiles = append(cxxfiles, outCXX...)
+	}
+
 	// Run cgo.
 	if p.UsesCgo() || p.UsesSwig() {
 		// In a package using cgo, cgo compiles the C, C++ and assembly files with gcc.
diff --git a/src/cmd/go/testdata/script/cover_swig.txt b/src/cmd/go/testdata/script/cover_swig.txt
new file mode 100644
index 0000000000..decb29aaec
--- /dev/null
+++ b/src/cmd/go/testdata/script/cover_swig.txt
@@ -0,0 +1,72 @@
+
+# Testcase for issue 64661.  This testcase is intended to verify that
+# we don't try to send swig-generated Go files through the cover tool
+# for "go test -cover" runs on packages that have *.swig source files.
+
+[!exec:swig] skip
+[!cgo] skip
+
+go test -v -count=1 -coverprofile=foo.p
+stdout 'coverage: 100.0% of statements'
+
+-- go.mod --
+module simple
+
+go 1.21
+-- main.c --
+/* A global variable */
+double Foo = 3.0;
+
+/* Compute the greatest common divisor of positive integers */
+int gcd(int x, int y) {
+  int g;
+  g = y;
+  while (x > 0) {
+    g = x;
+    x = y % x;
+    y = g;
+  }
+  return g;
+}
+
+
+-- main.go --
+package main
+
+import (
+	"fmt"
+)
+
+func main() {
+	// Call our gcd() function
+	x := 42
+	y := 105
+	g := Gcd(x, y)
+	fmt.Println("The gcd of", x, "and", y, "is", g)
+
+	// Manipulate the Foo global variable
+
+	// Output its current value
+	fmt.Println("Foo =", GetFoo())
+
+	// Change its value
+	SetFoo(3.1415926)
+
+	// See if the change took effect
+	fmt.Println("Foo =", GetFoo())
+}
+-- main.swig --
+%module main
+
+%inline %{
+extern int    gcd(int x, int y);
+extern double Foo;
+%}
+-- main_test.go --
+package main
+
+import "testing"
+
+func TestSwigFuncs(t *testing.T) {
+	main()
+}