"I don't think i have a shot at winning so I'll thank everyone here. I'm really grateful and proud as hell," she wrote. "Thank you Jerry Zaks for directing and encouraging me. Steve for your confidence in me and for writing this play. Getting to spend time with you laughing and listening to you play the banjo was heaven."
She went on to express appreciation for her co-stars Keegan-Michael Key, Laura Benanti and Jeremy Shamos, as well as her family and friends.
"And the audiences who came," she continued. "I've dreamt about being on broadway since I was a little idiot and man it delivered. The broadway community made me feel welcome and i think it's because they know how much love and respect i have for their work. Seeing theater is one of the greatest joys in my life."
Accompanying the message is a photo of Schumer in a store, holding up a Sgt. Bilko DVD -- priced at $2.99 and featuring Martin on the cover.
Schumer, 36, is up for Best Actress in a Play. She is competing against Glenda Jackson from Three Tall Women, Condola Rashad from Saint Joan and Lauren Ridloff from Children of a Lesser God.
Meteor Shower ran on Broadway Nov. 1, 2017 through Jan. 21, 2018.
Schumer was recently hospitalized for several days for a kidney infection.