The play is about two bears in an intergalactic space ship who have just thawed from cryogenic stasis, reported Entertainment Weekly.
Gleeson, 23, and a group of friends, whom he met while studying at Trinity College Dublin, created the surreal comedy for their theatre company.
"I don't really see this as acting. It's more like a fun project with friends," he said.
The play received acclaim at the Edinburgh Festival.
"Bears in Space" lands next at the Soho Theatre in London.