diff --git a/clippy_lints/src/methods/unnecessary_min_or_max.rs b/clippy_lints/src/methods/unnecessary_min_or_max.rs
index 86c0a6322b666..ff5fa7d33e3ee 100644
--- a/clippy_lints/src/methods/unnecessary_min_or_max.rs
+++ b/clippy_lints/src/methods/unnecessary_min_or_max.rs
@@ -1,16 +1,15 @@
 use std::cmp::Ordering;
 
 use super::UNNECESSARY_MIN_OR_MAX;
-use clippy_utils::diagnostics::span_lint_and_sugg;
-
 use clippy_utils::consts::{ConstEvalCtxt, Constant, ConstantSource, FullInt};
+use clippy_utils::diagnostics::span_lint_and_sugg;
 use clippy_utils::source::snippet;
 
 use rustc_errors::Applicability;
 use rustc_hir::Expr;
 use rustc_lint::LateContext;
 use rustc_middle::ty;
-use rustc_span::Span;
+use rustc_span::{sym, Span};
 
 pub(super) fn check<'tcx>(
     cx: &LateContext<'tcx>,
@@ -21,26 +20,30 @@ pub(super) fn check<'tcx>(
 ) {
     let typeck_results = cx.typeck_results();
     let ecx = ConstEvalCtxt::with_env(cx.tcx, cx.param_env, typeck_results);
-    if let Some((left, ConstantSource::Local | ConstantSource::CoreConstant)) = ecx.eval_with_source(recv)
-        && let Some((right, ConstantSource::Local | ConstantSource::CoreConstant)) = ecx.eval_with_source(arg)
+    if let Some(id) = typeck_results.type_dependent_def_id(expr.hir_id)
+        && (cx.tcx.is_diagnostic_item(sym::cmp_ord_min, id) || cx.tcx.is_diagnostic_item(sym::cmp_ord_max, id))
     {
-        let Some(ord) = Constant::partial_cmp(cx.tcx, typeck_results.expr_ty(recv), &left, &right) else {
-            return;
-        };
+        if let Some((left, ConstantSource::Local | ConstantSource::CoreConstant)) = ecx.eval_with_source(recv)
+            && let Some((right, ConstantSource::Local | ConstantSource::CoreConstant)) = ecx.eval_with_source(arg)
+        {
+            let Some(ord) = Constant::partial_cmp(cx.tcx, typeck_results.expr_ty(recv), &left, &right) else {
+                return;
+            };
 
-        lint(cx, expr, name, recv.span, arg.span, ord);
-    } else if let Some(extrema) = detect_extrema(cx, recv) {
-        let ord = match extrema {
-            Extrema::Minimum => Ordering::Less,
-            Extrema::Maximum => Ordering::Greater,
-        };
-        lint(cx, expr, name, recv.span, arg.span, ord);
-    } else if let Some(extrema) = detect_extrema(cx, arg) {
-        let ord = match extrema {
-            Extrema::Minimum => Ordering::Greater,
-            Extrema::Maximum => Ordering::Less,
-        };
-        lint(cx, expr, name, recv.span, arg.span, ord);
+            lint(cx, expr, name, recv.span, arg.span, ord);
+        } else if let Some(extrema) = detect_extrema(cx, recv) {
+            let ord = match extrema {
+                Extrema::Minimum => Ordering::Less,
+                Extrema::Maximum => Ordering::Greater,
+            };
+            lint(cx, expr, name, recv.span, arg.span, ord);
+        } else if let Some(extrema) = detect_extrema(cx, arg) {
+            let ord = match extrema {
+                Extrema::Minimum => Ordering::Greater,
+                Extrema::Maximum => Ordering::Less,
+            };
+            lint(cx, expr, name, recv.span, arg.span, ord);
+        }
     }
 }
 
diff --git a/tests/ui/unnecessary_min_or_max.fixed b/tests/ui/unnecessary_min_or_max.fixed
index 392f6dd1fee43..1f3e131516ce6 100644
--- a/tests/ui/unnecessary_min_or_max.fixed
+++ b/tests/ui/unnecessary_min_or_max.fixed
@@ -65,3 +65,32 @@ fn random_u32() -> u32 {
     // random number generator
     0
 }
+
+struct Issue13191 {
+    min: u16,
+    max: u16,
+}
+
+impl Issue13191 {
+    fn new() -> Self {
+        Self { min: 0, max: 0 }
+    }
+
+    fn min(mut self, value: u16) -> Self {
+        self.min = value;
+        self
+    }
+
+    fn max(mut self, value: u16) -> Self {
+        self.max = value;
+        self
+    }
+}
+
+fn issue_13191() {
+    // should not fixed
+    Issue13191::new().min(0);
+
+    // should not fixed
+    Issue13191::new().max(0);
+}
diff --git a/tests/ui/unnecessary_min_or_max.rs b/tests/ui/unnecessary_min_or_max.rs
index b03755e6d23d1..58356b9d49e77 100644
--- a/tests/ui/unnecessary_min_or_max.rs
+++ b/tests/ui/unnecessary_min_or_max.rs
@@ -65,3 +65,32 @@ fn random_u32() -> u32 {
     // random number generator
     0
 }
+
+struct Issue13191 {
+    min: u16,
+    max: u16,
+}
+
+impl Issue13191 {
+    fn new() -> Self {
+        Self { min: 0, max: 0 }
+    }
+
+    fn min(mut self, value: u16) -> Self {
+        self.min = value;
+        self
+    }
+
+    fn max(mut self, value: u16) -> Self {
+        self.max = value;
+        self
+    }
+}
+
+fn issue_13191() {
+    // should not fixed
+    Issue13191::new().min(0);
+
+    // should not fixed
+    Issue13191::new().max(0);
+}