diff --git a/ext/ArrayInterfaceCUDAExt.jl b/ext/ArrayInterfaceCUDAExt.jl
index 715f8107..7ba6216a 100644
--- a/ext/ArrayInterfaceCUDAExt.jl
+++ b/ext/ArrayInterfaceCUDAExt.jl
@@ -3,6 +3,7 @@ module ArrayInterfaceCUDAExt
 using ArrayInterface
 using CUDA
 using CUDA.CUSOLVER
+using CUDA.CUSPARSE
 using LinearAlgebra
 
 function ArrayInterface.lu_instance(A::CuMatrix{T}) where {T}
@@ -13,6 +14,17 @@ end
 
 ArrayInterface.device(::Type{<:CUDA.CuArray}) = ArrayInterface.GPU()
 
+# CUSPARSE arrays implement no `setindex!` at all, so the `true` default is wrong
+# for them and callers guarding mutation with `can_setindex` hit a CanonicalIndexError.
+const CuSparseArray = Union{
+    CUSPARSE.CuSparseVector,
+    CUSPARSE.CuSparseMatrixCSC,
+    CUSPARSE.CuSparseMatrixCSR,
+    CUSPARSE.CuSparseMatrixBSR,
+    CUSPARSE.CuSparseMatrixCOO,
+}
+ArrayInterface.can_setindex(::Type{<:CuSparseArray}) = false
+
 function ArrayInterface.promote_eltype(
         ::Type{<:CUDA.CuArray{T, N, M}}, ::Type{T2}
     ) where {T, N, M, T2}
diff --git a/test/gpu/cuda.jl b/test/gpu/cuda.jl
index 2651a638..b60c356e 100644
--- a/test/gpu/cuda.jl
+++ b/test/gpu/cuda.jl
@@ -18,3 +18,11 @@ lu_sparse = lu!(lu_inst_sparse, A_sparse)
 #test that the resulting lu works
 b = CuVector([1f0, 1f0])
 @test CUDA.@allowscalar lu_sparse \ b == [1, 1]
+
+# CUSPARSE arrays have no `setindex!`, so `can_setindex` must not claim they do
+@test ArrayInterface.can_setindex(A_dense)
+@test !ArrayInterface.can_setindex(A_sparse)
+@test !ArrayInterface.can_setindex(CuSparseMatrixCSC(sparse(A_cpu)))
+@test !ArrayInterface.can_setindex(CuSparseMatrixCOO(sparse(A_cpu)))
+@test !ArrayInterface.can_setindex(CuSparseVector(sparsevec([1], [1.0f0], 2)))
+@test_throws CanonicalIndexError A_sparse[1, 2] = 1.0f0