diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index af7dae030db..3b17c06c0e8 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -6917,6 +6917,13 @@ namespace ts {
 
                 if (isSimpleTypeRelatedTo(source, target, relation, reportErrors ? reportError : undefined)) return Ternary.True;
 
+                if (source.flags & TypeFlags.Index) {
+                    // A keyof T is related to a union type containing both string and number
+                    if (maybeTypeOfKind(target, TypeFlags.String) && maybeTypeOfKind(target, TypeFlags.Number)) {
+                        return Ternary.True;
+                    }
+                }
+
                 if (getObjectFlags(source) & ObjectFlags.ObjectLiteral && source.flags & TypeFlags.FreshLiteral) {
                     if (hasExcessProperties(<FreshObjectLiteralType>source, target, reportErrors)) {
                         if (reportErrors) {