diff --git a/src/cmd/go/internal/modload/search.go b/src/cmd/go/internal/modload/search.go
index a08c01479f6d83..536f44037b7533 100644
--- a/src/cmd/go/internal/modload/search.go
+++ b/src/cmd/go/internal/modload/search.go
@@ -102,7 +102,7 @@ func matchPackages(ld *Loader, ctx context.Context, m *search.Match, tags map[st
 			} else {
 				// Avoid .foo, _foo, and testdata subdirectory trees.
 				_, elem = filepath.Split(pkgDir)
-				if strings.HasPrefix(elem, ".") || strings.HasPrefix(elem, "_") || elem == "testdata" {
+				if IsIgnoredDirectory(elem) {
 					want = false
 				} else if ignorePatternsMap[cleanRoot] != nil && ignorePatternsMap[cleanRoot].ShouldIgnore(relPkgDir) {
 					if cfg.BuildX {
@@ -231,7 +231,7 @@ func walkFromIndex(index *modindex.Module, importPathRoot string, isMatch, treeC
 		p := reldir
 		for {
 			elem, rest, found := strings.Cut(p, string(filepath.Separator))
-			if strings.HasPrefix(elem, ".") || strings.HasPrefix(elem, "_") || elem == "testdata" {
+			if IsIgnoredDirectory(elem) {
 				return
 			}
 			if found && elem == "vendor" {
@@ -358,3 +358,9 @@ func parseIgnorePatterns(ld *Loader, ctx context.Context, treeCanMatch func(stri
 	}
 	return ignorePatternsMap
 }
+
+// IsIgnoredDirectory checks whether the path element should be ignored.
+// That is, if it starts with '.' or '_' or is called 'testdata'.
+func IsIgnoredDirectory(pathElem string) bool {
+	return strings.HasPrefix(pathElem, ".") || strings.HasPrefix(pathElem, "_") || pathElem == "testdata"
+}
diff --git a/src/cmd/go/internal/test/test.go b/src/cmd/go/internal/test/test.go
index 2084bc68a91217..53cdbc26bdfaab 100644
--- a/src/cmd/go/internal/test/test.go
+++ b/src/cmd/go/internal/test/test.go
@@ -878,7 +878,10 @@ func runTest(ctx context.Context, cmd *base.Command, args []string) {
 	if cfg.BuildCoverPkg != nil {
 		match := make([]func(*modload.Loader, *load.Package) bool, len(cfg.BuildCoverPkg))
 		for i := range cfg.BuildCoverPkg {
-			match[i] = load.MatchPackage(cfg.BuildCoverPkg[i], base.Cwd())
+			match[i] = func(l *modload.Loader, p *load.Package) bool {
+				cwd := base.Cwd()
+				return load.MatchPackage(cfg.BuildCoverPkg[i], cwd)(l, p) && !isUnderSpecial(cwd, p.Dir)
+			}
 		}
 
 		// Select for coverage all dependencies matching the -coverpkg
@@ -2311,3 +2314,19 @@ func testBinaryName(p *load.Package) string {
 
 	return elem + ".test"
 }
+
+// isUnderSpecial checks whether dir is contained within a 'special' directory under 'cwd'.
+// A directory is special if it beings with "." or "_" , or is called "testdata"
+func isUnderSpecial(cwd string, dir string) bool {
+	rel, err := filepath.Rel(cwd, dir)
+	if err != nil {
+		return false
+	}
+
+	sep := string(filepath.Separator)
+	pathComponents := strings.Split(rel, sep)
+	shouldIgnoreElemt := func(elem string) bool {
+		return modload.IsIgnoredDirectory(elem) && elem != "." && elem != ".."
+	}
+	return slices.IndexFunc(pathComponents, shouldIgnoreElemt) != -1
+}
diff --git a/src/cmd/go/testdata/script/coverpkg_ignores_special_dirs.txt b/src/cmd/go/testdata/script/coverpkg_ignores_special_dirs.txt
new file mode 100644
index 00000000000000..664cfbdfb4ca4a
--- /dev/null
+++ b/src/cmd/go/testdata/script/coverpkg_ignores_special_dirs.txt
@@ -0,0 +1,59 @@
+# test for https://github.com/golang/go/issues/66038
+[short] skip
+
+env GO111MODULE=off
+# files
+env GOPATH=$WORK/.dir${:}$WORK/_dir${:}$WORK/testdata
+
+cd $WORK
+go test -coverpkg=./... ./...
+stdout 'coverage: 100.0%'
+go test -coverpkg=. ./...
+stdout 'coverage: 100.0%'
+
+-- $WORK/a.go --
+package a
+
+// trivial function with 100% test coverage
+
+import (
+	_ "dot_dir"
+	_ "under_dir"
+	_ "testdata_dir"
+)
+
+func F(i int) int {
+	return i*i
+}
+
+-- $WORK/a_test.go --
+package a
+
+import (
+	"testing"
+)
+
+func TestF(t *testing.T) {
+	F(2)
+}
+
+-- $WORK/.dir/src/dot_dir/b.go --
+package dot_dir
+
+func G(i int) int {
+	return i*i
+}
+
+-- $WORK/_dir/src/under_dir/b.go --
+package dot_dir
+
+func G(i int) int {
+	return i*i
+}
+
+-- $WORK/testdata/src/testdata_dir/b.go --
+package testdata_dir
+
+func G(i int) int {
+	return i*i
+}