El Arbi shared several messages of support on social media including from Edgar Wright and Guardians Of The Galaxy director James Gunn.
It comes following the shock announcement that Warner Bros was shelving the multi-million dollar movie, which was filmed entirely in Glasgow, five months before its scheduled release.
In January, the Trongate area of Glasgow was transformed by set builders into Gotham City with alterations made to shop fronts and police cars.
Batgirl was due to focus on Barbara Gordon, the daughter of Gotham police commissioner Jim Gordon.
El Arbi and his co-director Bilall Fallah said they were “shocked and saddened” at the news, having found it out while at a wedding together.
“Thanks for all the messages of support all over the world,” El Arbi wrote on his Instagram story.
“Shoutout to directors @edgarwright & @jamesgunn… your kind words and experience mean a lot and help us through this difficult period.”
In another post he shared a screenshot of an email from Feige, which read: “My friends I had to reach out and let you know we are all thinking about you both.
“Because of the wonderful news about the wedding (congrats!) and the disappointing news about Batgirl.
“Very proud of you guys for all the amazing work you do and particularly Ms. Marvel of course!
“Can’t wait to see what is next for you. Hope to see you soon.”
Batgirl was due to feature Hollywood stars Michael Keaton, Brendan Fraser, JK Simmons and Leslie Grace, and reportedly cost an estimated 70 million dollars (£57.6 million)
The film was scheduled for release in late 2022 but was reportedly dropped after poor test screenings.
It comes as Warner Bros bosses said they are considering a restructure of the DC superhero franchise and the implementation of a 10-year plan, to emulate the success of their Marvel competitors.
Chief executive David Zaslav said the company would focus on the “quality” of upcoming blockbusters in order to “protect the DC brand”.