diff --git a/stdlib/LinearAlgebra/src/dense.jl b/stdlib/LinearAlgebra/src/dense.jl
index 683f7e45cb28d..91c38e7f0b09b 100644
--- a/stdlib/LinearAlgebra/src/dense.jl
+++ b/stdlib/LinearAlgebra/src/dense.jl
@@ -106,6 +106,11 @@ norm1(x::Union{Array{T},StridedVector{T}}) where {T<:BlasReal} =
 norm2(x::Union{Array{T},StridedVector{T}}) where {T<:BlasFloat} =
     length(x) < NRM2_CUTOFF ? generic_norm2(x) : BLAS.nrm2(x)
 
+# Conservative assessment of types that have zero(T) defined for themselves
+haszero(::Type) = false
+haszero(::Type{T}) where {T<:Number} = isconcretetype(T)
+@propagate_inbounds _zero(M::AbstractArray{T}, i, j) where {T} = haszero(T) ? zero(T) : zero(M[i,j])
+
 """
     triu!(M, k::Integer)
 
@@ -136,7 +141,7 @@ function triu!(M::AbstractMatrix, k::Integer)
     m, n = size(M)
     for j in 1:min(n, m + k)
         for i in max(1, j - k + 1):m
-            @inbounds M[i,j] = zero(M[i,j])
+            @inbounds M[i,j] = _zero(M, i,j)
         end
     end
     M
@@ -173,12 +178,13 @@ function tril!(M::AbstractMatrix, k::Integer)
     require_one_based_indexing(M)
     m, n = size(M)
     for j in max(1, k + 1):n
-        @inbounds for i in 1:min(j - k - 1, m)
-            M[i,j] = zero(M[i,j])
+        for i in 1:min(j - k - 1, m)
+            @inbounds M[i,j] = _zero(M, i,j)
         end
     end
     M
 end
+
 tril(M::Matrix, k::Integer) = tril!(copy(M), k)
 
 """
diff --git a/stdlib/LinearAlgebra/test/triangular.jl b/stdlib/LinearAlgebra/test/triangular.jl
index 43cafaaa74c9e..d8948ae109735 100644
--- a/stdlib/LinearAlgebra/test/triangular.jl
+++ b/stdlib/LinearAlgebra/test/triangular.jl
@@ -897,6 +897,35 @@ end
     end
 end
 
+@testset "tril!/triu! for non-bitstype matrices" begin
+    @testset "numeric" begin
+        M = Matrix{BigFloat}(undef, 3, 3)
+        tril!(M)
+        L = LowerTriangular(ones(3,3))
+        copytrito!(M, L, 'L')
+        @test M == L
+
+        M = Matrix{BigFloat}(undef, 3, 3)
+        triu!(M)
+        U = UpperTriangular(ones(3,3))
+        copytrito!(M, U, 'U')
+        @test M == U
+    end
+    @testset "array elements" begin
+        M = fill(ones(2,2), 4, 4)
+        tril!(M)
+        L = LowerTriangular(fill(fill(2,2,2),4,4))
+        copytrito!(M, L, 'L')
+        @test M == L
+
+        M = fill(ones(2,2), 4, 4)
+        triu!(M)
+        U = UpperTriangular(fill(fill(2,2,2),4,4))
+        copytrito!(M, U, 'U')
+        @test M == U
+    end
+end
+
 @testset "avoid matmul ambiguities with ::MyMatrix * ::AbstractMatrix" begin
     A = [i+j for i in 1:2, j in 1:2]
     S = SizedArrays.SizedArray{(2,2)}(A)