diff --git a/src/Utilities/matrix_of_constraints.jl b/src/Utilities/matrix_of_constraints.jl
index 622a0eafa7..f48b5a0f33 100644
--- a/src/Utilities/matrix_of_constraints.jl
+++ b/src/Utilities/matrix_of_constraints.jl
@@ -314,3 +314,20 @@ function final_touch(model::MatrixOfConstraints, index_map)
     empty!(model.caches)
     return
 end
+
+# Users of `MatrixOfConstraints` assume variable indices to be `1:n` where `n`
+# is the number of columns so we don't support variable deletion.
+function _throw_if_cannot_delete(
+    ::MatrixOfConstraints,
+    ::Vector{MOI.VariableIndex},
+    vi::MOI.VariableIndex,
+)
+    return throw(MOI.DeleteNotAllowed(vi))
+end
+function _throw_if_cannot_delete(
+    ::MatrixOfConstraints,
+    vis::Vector{MOI.VariableIndex},
+    ::Set{MOI.VariableIndex},
+)
+    return throw(MOI.DeleteNotAllowed(first(vis)))
+end
diff --git a/src/Utilities/model.jl b/src/Utilities/model.jl
index 614a83af7a..15ab2927d4 100644
--- a/src/Utilities/model.jl
+++ b/src/Utilities/model.jl
@@ -129,9 +129,11 @@ function _delete_variable(
         MOI.ConstraintIndex{MOI.SingleVariable,MOI.Semiinteger{T}}(vi.value),
     )
 end
+_fast_in(vi1::MOI.VariableIndex, vi2::MOI.VariableIndex) = vi1 == vi2
+_fast_in(vi::MOI.VariableIndex, vis::Set{MOI.VariableIndex}) = vi in vis
 function MOI.delete(model::AbstractModel, vi::MOI.VariableIndex)
     vis = [vi]
-    _throw_if_cannot_delete(model.constraints, vis, vis)
+    _throw_if_cannot_delete(model.constraints, vis, vi)
     _delete_variable(model, vi)
     _deleted_constraints(model.constraints, vi) do ci
         return delete!(model.con_to_name, ci)
diff --git a/src/Utilities/universalfallback.jl b/src/Utilities/universalfallback.jl
index ef133ef133..afc38fc224 100644
--- a/src/Utilities/universalfallback.jl
+++ b/src/Utilities/universalfallback.jl
@@ -204,7 +204,7 @@ end
 function MOI.delete(uf::UniversalFallback, vi::MOI.VariableIndex)
     vis = [vi]
     for constraints in values(uf.constraints)
-        _throw_if_cannot_delete(constraints, vis, vis)
+        _throw_if_cannot_delete(constraints, vis, vi)
     end
     MOI.delete(uf.model, vi)
     for d in values(uf.varattr)
diff --git a/src/Utilities/vector_of_constraints.jl b/src/Utilities/vector_of_constraints.jl
index 0373801163..286a0bbfb6 100644
--- a/src/Utilities/vector_of_constraints.jl
+++ b/src/Utilities/vector_of_constraints.jl
@@ -186,7 +186,7 @@ function _throw_if_cannot_delete(
         f = fs[1]::MOI.VectorOfVariables
         if length(f.variables) > 1 && f.variables != vis
             for vi in f.variables
-                if vi in fast_in_vis
+                if _fast_in(vi, fast_in_vis)
                     # If `supports_dimension_update(S)` then the variable
                     # will be removed in `_filter_variables`.
                     throw_delete_variable_in_vov(vi)
diff --git a/test/Utilities/matrix_of_constraints.jl b/test/Utilities/matrix_of_constraints.jl
index 33bffbbee6..d235c8fec9 100644
--- a/test/Utilities/matrix_of_constraints.jl
+++ b/test/Utilities/matrix_of_constraints.jl
@@ -218,6 +218,14 @@ MOIU.@product_of_sets(
             false,
             Indexing,
         ) do optimizer
+            vis = MOI.get(optimizer, MOI.ListOfVariableIndices())
+            @test_throws MOI.DeleteNotAllowed(first(vis)) MOI.delete(
+                optimizer,
+                vis,
+            )
+            for vi in vis
+                @test_throws MOI.DeleteNotAllowed(vi) MOI.delete(optimizer, vi)
+            end
             con_types = [
                 (F, MOI.EqualTo{Float64}),
                 (F, MOI.GreaterThan{Float64}),
@@ -234,6 +242,10 @@ MOIU.@product_of_sets(
                 for ci in cis
                     @test MOI.is_valid(optimizer, ci)
                     @test i == MOI.Utilities.rows(optimizer.constraints, ci)
+                    @test_throws MOI.DeleteNotAllowed(ci) MOI.delete(
+                        optimizer,
+                        ci,
+                    )
                 end
             end
         end