diff --git a/mlir/include/mlir/Dialect/AffineOps/AffineOps.td b/mlir/include/mlir/Dialect/AffineOps/AffineOps.td
--- a/mlir/include/mlir/Dialect/AffineOps/AffineOps.td
+++ b/mlir/include/mlir/Dialect/AffineOps/AffineOps.td
@@ -238,13 +238,25 @@
     Op<Affine_Dialect, mnemonic, traits> {
   let arguments = (ins AffineMapAttr:$map, Variadic<Index>:$operands);
   let results = (outs Index);
+
+  let builders = [
+    OpBuilder<"Builder *builder, OperationState &result, AffineMap affineMap, "
+              "ValueRange mapOperands",
+    [{
+      build(builder, result, builder->getIndexType(), affineMap, mapOperands);
+    }]>
+  ];
+
   let extraClassDeclaration = [{
     static StringRef getMapAttrName() { return "map"; }
+    AffineMap getAffineMap() { return map(); }
+    ValueRange getMapOperands() { return operands(); }
   }];
   let verifier = [{ return ::verifyAffineMinMaxOp(*this); }];
   let printer = [{ return ::printAffineMinMaxOp(p, *this); }];
   let parser = [{ return ::parseAffineMinMaxOp<$cppClass>(parser, result); }];
   let hasFolder = 1;
+  let hasCanonicalizer = 1;
 }
 
 def AffineMinOp : AffineMinMaxOpBase<"min", [NoSideEffect]> {
diff --git a/mlir/lib/Dialect/AffineOps/AffineOps.cpp b/mlir/lib/Dialect/AffineOps/AffineOps.cpp
--- a/mlir/lib/Dialect/AffineOps/AffineOps.cpp
+++ b/mlir/lib/Dialect/AffineOps/AffineOps.cpp
@@ -763,7 +763,9 @@
     static_assert(std::is_same<AffineOpTy, AffineLoadOp>::value ||
                       std::is_same<AffineOpTy, AffinePrefetchOp>::value ||
                       std::is_same<AffineOpTy, AffineStoreOp>::value ||
-                      std::is_same<AffineOpTy, AffineApplyOp>::value,
+                      std::is_same<AffineOpTy, AffineApplyOp>::value ||
+                      std::is_same<AffineOpTy, AffineMinOp>::value ||
+                      std::is_same<AffineOpTy, AffineMaxOp>::value,
                   "affine load/store/apply op expected");
     auto map = affineOp.getAffineMap();
     AffineMap oldMap = map;
@@ -804,11 +806,13 @@
   rewriter.replaceOpWithNewOp<AffineStoreOp>(
       store, store.getValueToStore(), store.getMemRef(), map, mapOperands);
 }
-template <>
-void SimplifyAffineOp<AffineApplyOp>::replaceAffineOp(
-    PatternRewriter &rewriter, AffineApplyOp apply, AffineMap map,
+
+// Generic version for ops that don't have extra operands.
+template <typename AffineOpTy>
+void SimplifyAffineOp<AffineOpTy>::replaceAffineOp(
+    PatternRewriter &rewriter, AffineOpTy op, AffineMap map,
     ArrayRef<Value> mapOperands) const {
-  rewriter.replaceOpWithNewOp<AffineApplyOp>(apply, map, mapOperands);
+  rewriter.replaceOpWithNewOp<AffineOpTy>(op, map, mapOperands);
 }
 } // end anonymous namespace.
 
@@ -2016,6 +2020,11 @@
   return results[minIndex];
 }
 
+void AffineMinOp::getCanonicalizationPatterns(
+    OwningRewritePatternList &patterns, MLIRContext *context) {
+  patterns.insert<SimplifyAffineOp<AffineMinOp>>(context);
+}
+
 //===----------------------------------------------------------------------===//
 // AffineMaxOp
 //===----------------------------------------------------------------------===//
@@ -2046,6 +2055,11 @@
   return results[maxIndex];
 }
 
+void AffineMaxOp::getCanonicalizationPatterns(
+    OwningRewritePatternList &patterns, MLIRContext *context) {
+  patterns.insert<SimplifyAffineOp<AffineMaxOp>>(context);
+}
+
 //===----------------------------------------------------------------------===//
 // AffinePrefetchOp
 //===----------------------------------------------------------------------===//
diff --git a/mlir/test/AffineOps/canonicalize.mlir b/mlir/test/AffineOps/canonicalize.mlir
--- a/mlir/test/AffineOps/canonicalize.mlir
+++ b/mlir/test/AffineOps/canonicalize.mlir
@@ -551,4 +551,20 @@
   // CHECK-NEXT:  "op0"(%[[CST]]) : (index) -> ()
   // CHECK-NEXT:  return
   return
-}
\ No newline at end of file
+}
+
+// -----
+
+// CHECK: #[[map:.*]] = affine_map<(d0, d1) -> (d0, d1 - 2)>
+
+func @affine_min(%arg0: index) {
+  affine.for %i = 0 to %arg0 {
+    affine.for %j = 0 to %arg0 {
+      %c2 = constant 2 : index
+      // CHECK: affine.min #[[map]]
+      %0 = affine.min affine_map<(d0,d1,d2)->(d0, d1 - d2)>(%i, %j, %c2)
+      "consumer"(%0) : (index) -> ()
+    }
+  }
+  return
+}