diff --git a/src/Utilities/distance_to_set.jl b/src/Utilities/distance_to_set.jl
index 44dcdb85de..045bfddebc 100644
--- a/src/Utilities/distance_to_set.jl
+++ b/src/Utilities/distance_to_set.jl
@@ -557,3 +557,25 @@ function distance_to_set(
     eigvals .= min.(zero(T), eigvals)
     return LinearAlgebra.norm(eigvals, 2)
 end
+
+"""
+    distance_to_set(
+        ::ProjectionUpperBoundDistance,
+        x::AbstractVector{T},
+        set::MOI.VectorNonlinearOracle,
+    ) where {T<:Real}
+
+!!! warning
+    This is not an upper bound on the projection in `x` space; instead, it
+    is a projection in `f(x)`-space.
+"""
+function distance_to_set(
+    ::ProjectionUpperBoundDistance,
+    x::AbstractVector{T},
+    set::MOI.VectorNonlinearOracle{T},
+) where {T<:Real}
+    _check_dimension(x, set)
+    y = zeros(T, set.output_dimension)
+    set.eval_f(y, x)
+    return LinearAlgebra.norm(y .- clamp.(y, set.l, set.u))
+end
diff --git a/test/Utilities/distance_to_set.jl b/test/Utilities/distance_to_set.jl
index ba28a0baa9..411b1cfd71 100644
--- a/test/Utilities/distance_to_set.jl
+++ b/test/Utilities/distance_to_set.jl
@@ -338,6 +338,44 @@ function test_positivesemidefiniteconetriangle()
     return
 end
 
+function test_vectornonlinearoracle()
+    function eval_f(ret::AbstractVector, x::AbstractVector)
+        ret[1] = sum(x)
+        ret[2] = x[1]^2 + x[2]^2 - x[3]^2
+        ret[3] = x[1]^2 - x[2] * x[3]
+        return
+    end
+    function eval_jacobian(ret::AbstractVector, x::AbstractVector)
+        ret[1] = 1.0
+        ret[2] = 1.0
+        ret[3] = 1.0
+        ret[4] = 2.0 * x[1]
+        ret[5] = 2.0 * x[2]
+        ret[6] = -2.0 * x[3]
+        ret[7] = 2.0 * x[1]
+        ret[8] = -1.0 * x[3]
+        ret[9] = -1.0 * x[2]
+        return
+    end
+    set = MOI.VectorNonlinearOracle(;
+        dimension = 3,
+        l = [1.0, -Inf, -Inf],
+        u = [1.0, 0.0, 0.0],
+        eval_f,
+        jacobian_structure = [(i, j) for i in 1:3 for j in 1:3],
+        eval_jacobian,
+    )
+    _test_set(
+        set,
+        [0.0, 0.0, 0.0] => 1.0,
+        [1.0, 0.0, 0.0] => sqrt(2),
+        [0.0, 1.0, 0.0] => 1.0,
+        [0.0, 0.0, 1.0] => 0.0,
+        mismatch = [1.0],
+    )
+    return
+end
+
 end
 
 TestFeasibilityChecker.runtests()