diff --git a/stdlib/LinearAlgebra/src/matmul.jl b/stdlib/LinearAlgebra/src/matmul.jl
index 4fed8a577bd638..27bd9c2f23b153 100644
--- a/stdlib/LinearAlgebra/src/matmul.jl
+++ b/stdlib/LinearAlgebra/src/matmul.jl
@@ -823,7 +823,7 @@ function _generic_matmatmul!(C::AbstractVecOrMat{R}, tA, tB, A::AbstractVecOrMat
 
     tile_size = 0
     if isbitstype(R) && isbitstype(T) && isbitstype(S) && (tA == 'N' || tB != 'N')
-        tile_size = floor(Int, sqrt(tilebufsize / max(sizeof(R), sizeof(S), sizeof(T))))
+        tile_size = floor(Int, sqrt(tilebufsize / max(sizeof(R), sizeof(S), sizeof(T), 1)))
     end
     @inbounds begin
     if tile_size > 0
diff --git a/stdlib/LinearAlgebra/test/matmul.jl b/stdlib/LinearAlgebra/test/matmul.jl
index 6a81222174e1fe..107c579ba1f942 100644
--- a/stdlib/LinearAlgebra/test/matmul.jl
+++ b/stdlib/LinearAlgebra/test/matmul.jl
@@ -720,6 +720,16 @@ end
     @test D ≈ C
 end
 
+@testset "size zero types in matrix mult (see issue 39362)" begin
+    A = [missing missing; missing missing]
+    v = [missing, missing]
+    @test (A * v == v) === missing
+    M = fill(1.0, 2, 2)
+    a = fill(missing, 2, 1)
+    @test (a' * M * a == fill(missing,1,1)) === missing
+end
+
+
 @testset "multiplication of empty matrices without calling zero" begin
     r, c = rand(0:9, 2)
     A = collect(Number, rand(r, c))