diff --git a/var/spack/repos/builtin/packages/mfem/package.py b/var/spack/repos/builtin/packages/mfem/package.py
index 0fa5c7f3b76..5b3bc166ff0 100644
--- a/var/spack/repos/builtin/packages/mfem/package.py
+++ b/var/spack/repos/builtin/packages/mfem/package.py
@@ -198,6 +198,9 @@ class Mfem(Package, CudaPackage, ROCmPackage):
     conflicts('+pumi', when='~mpi')
     conflicts('timer=mpi', when='~mpi')
 
+    # See https://github.com/mfem/mfem/issues/2957
+    conflicts('^mpich@4:', when='+mpi')
+
     depends_on('mpi', when='+mpi')
     depends_on('hypre@2.10.0:2.13', when='@:3.3+mpi')
     depends_on('hypre@:2.20.0', when='@3.4:4.2+mpi')