Schumer and Fischer first began dating in November last year, and have seemingly made a concerted effort to ensure that their burgeoning romance had remained out of the spotlight.
Unusually, Schumer recently posted a photograph on her Instagram account of her and Fisher - who is a chef - sharing a kiss at TV star Ellen DeGeneres' birthday party.
By contrast, Schumer's previous relationship with Ben Hanisch - which ended in May 2017 - was noticeably more high-profile.
The blonde star revealed prior to their split that she was "in love" with her then-boyfriend.
She said: "We met and, like, totally fell in love and it's been really good, and it became viral Internet news.
"I think it's because he's really cute and people were like, 'What? Dating Amy? He has all his teeth!' Like, people were shocked. They were shocked."
The Trainwreck star also spoke of her ambition to start a family.
She explained: "I love the idea of committing to somebody and making that choice. I want to have a family, I think, and everything. But right now, we're not in talks."
However, the Hollywood star also admitted that being in love with someone caused her to feel under pressure.
Schumer previously confessed: "Being in love is the scariest thing in the world.
"You want to f**king cry and scream. I can't handle it. Every time we say goodbye, I think, 'This will have been a nice last week together.' Or I tell myself nothing is real and he's going to leave me and tell me he never loved me.' I feel so bad for him. How exhausting it must be dating me."
- Bang! Showbiz
