diff --git a/Misc/NEWS.d/next/Build/2024-11-06-11-12-04.gh-issue-126458.7vzHtx.rst b/Misc/NEWS.d/next/Build/2024-11-06-11-12-04.gh-issue-126458.7vzHtx.rst
new file mode 100644
index 00000000000..cc06dd8a30e
--- /dev/null
+++ b/Misc/NEWS.d/next/Build/2024-11-06-11-12-04.gh-issue-126458.7vzHtx.rst
@@ -0,0 +1 @@
+Disable SIMD support for HACL under WASI.
diff --git a/configure b/configure
index e529527214d..e0ab304570d 100755
--- a/configure
+++ b/configure
@@ -30770,7 +30770,8 @@ esac
 
 # The SIMD files use aligned_alloc, which is not available on older versions of
 # Android.
-if test "$ac_sys_system" != "Linux-android" || test "$ANDROID_API_LEVEL" -ge 28; then
+# The *mmintrin.h headers are x86-family-specific, so can't be used on WASI.
+if test "$ac_sys_system" != "Linux-android" -a "$ac_sys_system" != "WASI" || test "$ANDROID_API_LEVEL" -ge 28; then
     { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking whether C compiler accepts -msse -msse2 -msse3 -msse4.1 -msse4.2" >&5
 printf %s "checking whether C compiler accepts -msse -msse2 -msse3 -msse4.1 -msse4.2... " >&6; }
 if test ${ax_cv_check_cflags__Werror__msse__msse2__msse3__msse4_1__msse4_2+y}
@@ -30837,11 +30838,12 @@ fi
 
 # The SIMD files use aligned_alloc, which is not available on older versions of
 # Android.
+# The *mmintrin.h headers are x86-family-specific, so can't be used on WASI.
 #
 # Although AVX support is not guaranteed on Android
 # (https://developer.android.com/ndk/guides/abis#86-64), this is safe because we do a
 # runtime CPUID check.
-if test "$ac_sys_system" != "Linux-android" || test "$ANDROID_API_LEVEL" -ge 28; then
+if test "$ac_sys_system" != "Linux-android" -a "$ac_sys_system" != "WASI" || test "$ANDROID_API_LEVEL" -ge 28; then
   { printf "%s\n" "$as_me:${as_lineno-$LINENO}: checking whether C compiler accepts -mavx2" >&5
 printf %s "checking whether C compiler accepts -mavx2... " >&6; }
 if test ${ax_cv_check_cflags__Werror__mavx2+y}
diff --git a/configure.ac b/configure.ac
index bc67a0596ac..da7d1ef68ee 100644
--- a/configure.ac
+++ b/configure.ac
@@ -7853,7 +7853,8 @@ AC_SUBST([LIBHACL_CFLAGS])
 
 # The SIMD files use aligned_alloc, which is not available on older versions of
 # Android.
-if test "$ac_sys_system" != "Linux-android" || test "$ANDROID_API_LEVEL" -ge 28; then
+# The *mmintrin.h headers are x86-family-specific, so can't be used on WASI.
+if test "$ac_sys_system" != "Linux-android" -a "$ac_sys_system" != "WASI" || test "$ANDROID_API_LEVEL" -ge 28; then
   dnl This can be extended here to detect e.g. Power8, which HACL* should also support.
   AX_CHECK_COMPILE_FLAG([-msse -msse2 -msse3 -msse4.1 -msse4.2],[
     [LIBHACL_SIMD128_FLAGS="-msse -msse2 -msse3 -msse4.1 -msse4.2"]
@@ -7879,11 +7880,12 @@ AC_SUBST([LIBHACL_SIMD128_OBJS])
 
 # The SIMD files use aligned_alloc, which is not available on older versions of
 # Android.
+# The *mmintrin.h headers are x86-family-specific, so can't be used on WASI.
 #
 # Although AVX support is not guaranteed on Android
 # (https://developer.android.com/ndk/guides/abis#86-64), this is safe because we do a
 # runtime CPUID check.
-if test "$ac_sys_system" != "Linux-android" || test "$ANDROID_API_LEVEL" -ge 28; then
+if test "$ac_sys_system" != "Linux-android" -a "$ac_sys_system" != "WASI" || test "$ANDROID_API_LEVEL" -ge 28; then
   AX_CHECK_COMPILE_FLAG([-mavx2],[
     [LIBHACL_SIMD256_FLAGS="-mavx2"]
     AC_DEFINE([HACL_CAN_COMPILE_SIMD256], [1], [HACL* library can compile SIMD256 implementations])