diff --git a/base/sharedarray.jl b/base/sharedarray.jl
index fa9d42412c966..65d95ed7f2e8c 100644
--- a/base/sharedarray.jl
+++ b/base/sharedarray.jl
@@ -89,7 +89,7 @@ function SharedArray(T::Type, dims::NTuple; init=false, pids=Int[])
         end
 
         # All good, immediately unlink the segment.
-        if prod(dims) > 0
+        if (prod(dims) > 0) && (sizeof(T) > 0)
             if onlocalhost
                 rc = shm_unlink(shm_seg_name)
             else
@@ -508,7 +508,7 @@ function shm_mmap_array(T, dims, shm_seg_name, mode)
     local s = nothing
     local A = nothing
 
-    if prod(dims) == 0
+    if (prod(dims) == 0) || (sizeof(T) == 0)
         return Array{T}(dims)
     end
 
diff --git a/test/parallel_exec.jl b/test/parallel_exec.jl
index 2e5ba5f35c7df..ecb89640b32ed 100644
--- a/test/parallel_exec.jl
+++ b/test/parallel_exec.jl
@@ -452,6 +452,13 @@ map!(x->1, d)
 @test 2.0 == remotecall_fetch(D->D[2], id_other, Base.shmem_fill(2.0, 2; pids=[id_me, id_other]))
 @test 3.0 == remotecall_fetch(D->D[1], id_other, Base.shmem_fill(3.0, 1; pids=[id_me, id_other]))
 
+# Shared arrays of singleton immutables
+@everywhere immutable ShmemFoo end
+for T in [Void, ShmemFoo]
+    s = SharedArray(T, 10)
+    @test T() === remotecall_fetch(x->x[3], workers()[1], s)
+end
+
 # Issue #14664
 d = SharedArray(Int,10)
 @sync @parallel for i=1:10