The Friends actor, 56, shared a photo of them hugging on Sunday, 2 November, captioning it “Happy birthday my love” with a red heart emoji.
Aniston and Curtis have been romantically linked since July, with Curtis later sharing a newsletter about finding “joy” and “magic” after a holiday with Aniston and friends.
Aniston has previously spoken about her 20-year struggle to have children, including unsuccessful IVF attempts, and her decision against adoption.
She also criticised the media's speculation and scrutiny regarding her childless status, refuting the “selfish workaholic” narrative.