The actor was due to host Fall Formal for his online collaborative production site, HitRECord.org, at New York City's Town Hall Theater on 28 October (10), but the event has been called off in the wake of the tragedy.
Gordon-Levitt has released a statement explaining the cancellation, admitting he is struggling to cope and feels "less than capable" of doing any work.
In a message on his website, he writes, "I have some regrettable news regarding the Fall Formal. As you might know, these past two weeks have been the worst of my life. To those contributing tribute RECords re: my brother Dan, you have my deepest gratitude.
"I'm eager to get back to work, but I also feel like I've just had an arm chopped off and so I'm finding myself less than capable these days.
"I've considered various possibilities on how to make the show happen another way - the Town Hall Theater has been so accommodating in figuring this out with us. But in the end, I just don't feel up to it right now and have decided to cancel the show.
"Chin up, there's still much to do and a bright future ahead."
Tickets purchased for the gala will be refunded in full.