diff --git a/src/Test/test_model.jl b/src/Test/test_model.jl
index a6936e635b..520b295035 100644
--- a/src/Test/test_model.jl
+++ b/src/Test/test_model.jl
@@ -10,6 +10,7 @@ MOI.constant(set::UnknownScalarSet) = set.constant
 
 Base.copy(set::UnknownScalarSet) = UnknownScalarSet(copy(MOI.constant(set)))
 
+MOIU.supports_shift_constant(::Type{<:UnknownScalarSet}) = true
 function MOIU.shift_constant(set::UnknownScalarSet, offset)
     return UnknownScalarSet(MOI.constant(set) + offset)
 end
diff --git a/src/Utilities/constraints.jl b/src/Utilities/constraints.jl
index eed872458f..2f665135bd 100644
--- a/src/Utilities/constraints.jl
+++ b/src/Utilities/constraints.jl
@@ -51,10 +51,12 @@ function normalize_constant(
     set::MOI.AbstractScalarSet;
     allow_modify_function::Bool = false,
 ) where {T}
-    set = shift_constant(set, -func.constant)
-    if !allow_modify_function
-        func = copy(func)
+    if supports_shift_constant(typeof(set))
+        set = shift_constant(set, -func.constant)
+        if !allow_modify_function
+            func = copy(func)
+        end
+        func.constant = zero(T)
     end
-    func.constant = zero(T)
     return func, set
 end
diff --git a/test/Utilities/constraints.jl b/test/Utilities/constraints.jl
index fbc5fce73b..188d3d35b6 100644
--- a/test/Utilities/constraints.jl
+++ b/test/Utilities/constraints.jl
@@ -33,6 +33,10 @@ function test_normalize_and_add_constrant_ScalarAffineFunction()
     model = MOI.Utilities.Model{Float64}()
     x = MOI.add_variable(model)
     f = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 2.0)
+    int = MOI.Utilities.normalize_and_add_constraint(model, f, MOI.Integer())
+    @test f.constant == 2.0
+    @test MOI.get(model, MOI.ConstraintFunction(), int) ≈ f
+    @test MOI.get(model, MOI.ConstraintSet(), int) == MOI.Integer()
     g = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 0.0)
     ci = MOI.Utilities.normalize_and_add_constraint(model, f, MOI.EqualTo(3.0))
     @test f.constant == 2.0