diff --git a/mypy/build.py b/mypy/build.py
index c616faccadb37..5e26a511194f5 100644
--- a/mypy/build.py
+++ b/mypy/build.py
@@ -125,6 +125,7 @@
 from mypy.semanal_pass1 import SemanticAnalyzerPreAnalysis
 from mypy.util import (
     DecodeError,
+    can_start_threads,
     decode_python_encoding,
     get_available_threads,
     get_mypy_comments,
@@ -1021,8 +1022,8 @@ def parse_all(self, states: list[State], post_parse: bool = True) -> None:
         If post_parse is False, skip the last step (used when parsing unchanged files
         that need to be re-checked due to stale dependencies).
         """
-        if not self.options.native_parser:
-            # Old parser cannot be parallelized.
+        if not self.options.native_parser or not can_start_threads():
+            # Old parser cannot be parallelized, and some platforms don't support threads.
             for state in states:
                 state.parse_file()
             if post_parse:
diff --git a/mypy/util.py b/mypy/util.py
index a48a7ea824daf..5ad45af77e329 100644
--- a/mypy/util.py
+++ b/mypy/util.py
@@ -973,6 +973,15 @@ def json_loads(data: bytes) -> Any:
 _AVAILABLE_THREADS: int | None = None
 
 
+def can_start_threads() -> bool:
+    """Can we start new threads?
+
+    WebAssembly builds are typically single-threaded, and starting a thread
+    fails with RuntimeError there, so we must not even try.
+    """
+    return sys.platform not in ("emscripten", "wasi")
+
+
 def get_available_threads() -> int:
     """Determine number of physical cores that current process can use (best effort)."""
     global _AVAILABLE_THREADS
diff --git a/test-data/unit/fine-grained-blockers.test b/test-data/unit/fine-grained-blockers.test
index d201e4f07c941..48faa2cf7752b 100644
--- a/test-data/unit/fine-grained-blockers.test
+++ b/test-data/unit/fine-grained-blockers.test
@@ -522,7 +522,7 @@ a.py: error: Cannot decode file: 'ascii' codec can't decode byte 0xc3 in positio
 ==
 main:2: error: Argument 1 to "f" has incompatible type "int"; expected "str"
 
-[case testDecodeErrorBlockerOnInitialRun-posix]
+[case testDecodeErrorBlockerOnInitialRun-posix-skip]
 # Note that there's no test variant for Windows, since the above Windows test case is good enough.
 import a
 a.f(1)