diff --git a/src/cmd/go/internal/modload/query.go b/src/cmd/go/internal/modload/query.go
index 0359470d95..75c18f25cc 100644
--- a/src/cmd/go/internal/modload/query.go
+++ b/src/cmd/go/internal/modload/query.go
@@ -472,10 +472,10 @@ func queryPrefixModules(candidateModules []string, queryModule func(path string)
 					notExistErr = rErr
 				}
 			} else if err == nil {
-				if len(found) > 0 {
-					// golang.org/issue/34094: If we have already found a module
-					// containing the target package, ignore errors for modules with
-					// shorter paths.
+				if len(found) > 0 || noPackage != nil {
+					// golang.org/issue/34094: If we have already found a module that
+					// could potentially contain the target package, ignore unclassified
+					// errors for modules with shorter paths.
 
 					// golang.org/issue/34383 is a special case of this: if we have
 					// already found example.com/foo/v2@v2.0.0 with a matching go.mod
diff --git a/src/cmd/go/testdata/script/mod_get_major.txt b/src/cmd/go/testdata/script/mod_get_major.txt
index dd1cbe01a3..367ede9ded 100644
--- a/src/cmd/go/testdata/script/mod_get_major.txt
+++ b/src/cmd/go/testdata/script/mod_get_major.txt
@@ -13,6 +13,11 @@ go get -d vcs-test.golang.org/git/v3pkg.git/v3@v3.0.0
 go list -m vcs-test.golang.org/git/v3pkg.git/v3
 stdout '^vcs-test.golang.org/git/v3pkg.git/v3 v3.0.0$'
 
+go get -d vcs-test.golang.org/git/empty-v2-without-v1.git/v2@v2.0.0
+
+go list -m vcs-test.golang.org/git/empty-v2-without-v1.git/v2
+stdout '^vcs-test.golang.org/git/empty-v2-without-v1.git/v2 v2.0.0$'
+
 -- go.mod --
 module example.com
 go 1.13