diff --git a/src/Utilities/penalty_relaxation.jl b/src/Utilities/penalty_relaxation.jl
index 3521cc3cce..ed414225fb 100644
--- a/src/Utilities/penalty_relaxation.jl
+++ b/src/Utilities/penalty_relaxation.jl
@@ -142,6 +142,7 @@ end
     PenaltyRelaxation(
         penalties = Dict{MOI.ConstraintIndex,Float64}();
         default::Union{Nothing,T} = 1.0,
+        warn::Bool = true,
     )
 
 A problem modifier that, when passed to [`MOI.modify`](@ref), destructively
@@ -187,6 +188,9 @@ cannot be modified in-place.
 
 To modify variable bounds, rewrite them as linear constraints.
 
+If a constraint cannot be modified, a warning is logged and the
+constraint is skipped. The warning can be disabled by setting `warn = false`.
+
 ## Example
 
 ```jldoctest
@@ -242,12 +246,14 @@ true
 mutable struct PenaltyRelaxation{T}
     default::Union{Nothing,T}
     penalties::Dict{MOI.ConstraintIndex,T}
+    warn::Bool
 
     function PenaltyRelaxation(
         p::Dict{MOI.ConstraintIndex,T};
         default::Union{Nothing,T} = one(T),
+        warn::Bool = true,
     ) where {T}
-        return new{T}(default, p)
+        return new{T}(default, p, warn)
     end
 end
 
@@ -286,7 +292,11 @@ function _modify_penalty_relaxation(
             map[ci] = MOI.modify(model, ci, ScalarPenaltyRelaxation(penalty))
         catch err
             if err isa MethodError && err.f == MOI.modify
-                @warn("Skipping PenaltyRelaxation for ConstraintIndex{$F,$S}")
+                if relax.warn
+                    @warn(
+                        "Skipping PenaltyRelaxation for ConstraintIndex{$F,$S}"
+                    )
+                end
                 return
             end
             rethrow(err)
diff --git a/test/Utilities/penalty_relaxation.jl b/test/Utilities/penalty_relaxation.jl
index 226bf8a623..ae6c839f4b 100644
--- a/test/Utilities/penalty_relaxation.jl
+++ b/test/Utilities/penalty_relaxation.jl
@@ -65,6 +65,25 @@ function test_relax_bounds()
     return
 end
 
+function test_relax_no_warn()
+    input = """
+    variables: x, y
+    minobjective: x + y
+    x >= 0.0
+    y <= 0.0
+    x in ZeroOne()
+    y in Integer()
+    """
+    model = MOI.Utilities.Model{Float64}()
+    MOI.Utilities.loadfromstring!(model, input)
+    relaxation = MOI.Utilities.PenaltyRelaxation(; warn = false)
+    @test_logs MOI.modify(model, relaxation)
+    dest = MOI.Utilities.Model{Float64}()
+    MOI.Utilities.loadfromstring!(dest, input)
+    MOI.Bridges._test_structural_identical(model, dest)
+    return
+end
+
 function test_relax_affine_lessthan()
     _test_roundtrip(
         """