diff --git a/lib/fetch/headers.js b/lib/fetch/headers.js
index cfdc8868efa..69acaaad996 100644
--- a/lib/fetch/headers.js
+++ b/lib/fetch/headers.js
@@ -128,7 +128,7 @@ class HeadersList {
     if (init instanceof HeadersList) {
       this[kHeadersMap] = new Map(init[kHeadersMap])
       this[kHeadersSortedMap] = init[kHeadersSortedMap]
-      this.cookies = init.cookies
+      this.cookies = init.cookies === null ? null : [...init.cookies]
     } else {
       this[kHeadersMap] = new Map(init)
       this[kHeadersSortedMap] = null
diff --git a/test/fetch/request.js b/test/fetch/request.js
index acd3e6ab439..de593e8c053 100644
--- a/test/fetch/request.js
+++ b/test/fetch/request.js
@@ -487,4 +487,14 @@ test('request.referrer', (t) => {
   t.end()
 })
 
+// https://github.com/nodejs/undici/issues/2445
+test('Clone the set-cookie header when Request is passed as the first parameter and no header is passed.', (t) => {
+  t.plan(2)
+  const request = new Request('http://localhost', { headers: { 'set-cookie': 'A' } })
+  const request2 = new Request(request)
+  request2.headers.append('set-cookie', 'B')
+  t.equal(request.headers.getSetCookie().join(', '), request.headers.get('set-cookie'))
+  t.equal(request2.headers.getSetCookie().join(', '), request2.headers.get('set-cookie'))
+})
+
 teardown(() => process.exit())