Her husband Shirish Kunder, brother Sajid Khan and friend and designer Manish Malhotra have wished her a year full of happiness, luck and laughter.
Farah is a film director, producer, actress and choreographer. She is best known for her choreographic work in numerous Hindi films.
The 51-year-old has choreographed dance routines for more than a hundred songs in over 80 Hindi films.
She has worked on international projects such as "Marigold: An Adventure in India", "Monsoon Wedding" and the Chinese film "Perhaps Love".
She turned director in the 2004 film "Main Hoon Na", which starred superstar Shah Rukh Khan, who she has been good friends with.
In 2012, Farah made her film acting debut in a leading role in "Shirin Farhad Ki Toh Nikal Padi", directed by Bela Bhansali Sehgal.
Farah trained Colombian singer Shakira for a Bollywood version of her song "Hips Don't Lie" for the MTV Video Music Awards in 2006 and has also choreographed Kylie Minogue for the song "Chiggy Wiggy" in the 2009 movie "Blue".
Here's what the celebrities tweeted on her birthday:
Amitabh Bachchan: Happy birthday to theFarah Khan .. honest, clean and 'muh phat'
Also Read: Farah Khan turns 51: Here are some lesser known facts about the choreographer-turned-director
Shirish Kunder: Since tweeting is the only way I'll get to say 3 full words w/o being interrupted: Happy Birthday @TheFarahKhan
Karan Johar: Happy birthday my darling @TheFarahKhan....a lifetime of laughs...memories....and conversations.....love you!
Sajid Khan: Happy bday sis @TheFarahKhan.
Simi Garewal: Happy Birthday to my dearest @TheFarahKhan! A super woman/mom/wife/daughter/sister/filmmaker...and friend! Love you.
Shilpa Shetty Kundra: Happppy birthday my Darling , super mom ,amazing , fabulously funny, @thefarahkhan. Stay happy….
Sania Mirza: My most fav, who's been an older sister to me that I don't have. I love you... Thank you for being you. Happy birthday @TheFarahKhan.
Sujoy Ghosh: Happy birthday @TheFarahKhan ... sending across @VishalDadlani with pyaar, hugs and the works...
Manoj Bajpayee: You can be real and yet you can be successful. Happy birthday to one the most real and yet so successful friend neighbour @TheFarahKhan
Manish Malhotra: Wishing my dearest friend @TheFarahKhan a very Happy Birthday
Sunidhi Chauhan: @TheFarahKhan Happy Birthday to the most 'Bindaas' woman I know! I love you! Big hug and kisses.
Riteish Deshmukh: Happy Birthday my deaaarestt faruu @TheFarahKhan - Ek gulab hamari aur se (one rose from me) @geneliad
Lara Dutta: Happy Birthday dearest Farah! @TheFarahKhan. Have the superest duperest year! Big Hug!
Sonu Sood: @TheFarahKhan Happy birthday my best buddy. Missing you today so much.
Ronit Roy: A very happy birthday to the very talented very warm very full of life @TheFarahKhan . Much love, Always.
Genelia Deshmukh: Happy birthday @TheFarahKhan ... We wish you all the love n happiness always.
Milap Zaveri: Happy birthday @TheFarahKhan May this be a Happy New Year for you full of Om Shaanti Om! Loads of love!
Huma Qureshi: Happy wala birthday @TheFarahKhan .. stay happy and lovedddd (judging from other tweets..is #eldersister going to trend aaj?) lol love you!
Kriti Sanon: Happiest birthday @TheFarahKhan... One of the sweetest and coolest women I've met in the industry! Love you!
Farah Khan Ali: Darling Farah, @TheFarahKhan wishing you a very happy birthday with lots of love light and luck. Be blessed.
Diandra Soares: Happiest happywalla birthday @TheFarahKhan. Have a super rocking birthday