I am a beginner at guitar. My friend recently told me that bending my fingers this way while playing a chord can cause damage to the fingers. I cant help playing this way because of force of habit.
Is it true that playing this way damages the fingers?
Can you recommend exercises to overcome this habit? 
In general, locked joints are slow joints. They take time to lock and time to unlock and in the mean time, other joints have to move larger units through a zigzagged tendon sheaf. So it's something that tends to be worth avoiding. It's a matter of finger strength and resisting the finger snapping into that position. That's not specific to guitar: for example, the pinky in the fingering hand of a violin is similarly susceptible to this kind of final joint lock.
Training your last finger joints is something you can habitually do with a tabletop and do not need to confine to instrument playing practice.
It looks like you are trying to play an open G maj chord but that's hard to tell from the pic. In general a collapsed finger joint is not proper. With practice and correct posture that should not happen. Of course there are exceptions to every rule and people have different body sizes and shapes. Sometimes deviations make certain fingering difficult.
There are some other issue with your hand that make the bent joint secondary.
Your second finger on the low E string is covering the A string and probably dampening that string. You want to hear the B (maj 3rd) of the G chord and that will not happen with your second finger touching the string under it. That finger should be more on the tip to provide clearance.
You pinky is curled up in your palm and that is not proper posture. You fingers should float over the finger board in a relaxed and comfortable manner, ready to land on the strings. Of course this is very hard for beginners to master. Fatigue and dependence of the fingers on each other lead to "floppy" fingers and curled up fingers. The ring and pinky are connected by tendons and curling the pinky under might be forcing the ring into an unnatural position. Try floating the pink next to the ring.
Your finger nail looks a little too long. If you clip the ring finger nail back you should be able to land on the tip rather that the pad, i.e. roll the ring finger up a little and that should unlock the joint.
Other than the nail being long I think that if you roll your entire hand forward a little all the other issues will correct themselves.
I am not a doctor, nor an academically trained musician who received formal posture education, but I'll try to answer. Also this is my first activity on here, so If I get anything wrong, please let me know.
Just a couple of observations:
1) Different peoples have different bodies. As an example, my fingers are physically unable to bend like that, while some of my friends can effortlessly do crazy things with their hands (I ignore if this difference is due to genetics, early-life habits or what else). Some of those appear to be unable to do normal things (keeping a finger straight, for example). If that hand position is what your body finds more natural, I guess you have a physiological trait I appear to lack, but this should be no cause of great concern, as far as I can tell.
2) Developing a good posture while playing is essential. This is not a finger issue only: the position of your wrist is a most important factor in order to develop good hand posture and avoid long term injury ("keep you wrist straight" is the mantra). This is not even a hand-only problem, the way you sit and how you keep your guitar can greatly effect how easily you can play. Also, keep an eye to your right wrist, too. The angle at which you keep your guitar plays an important role. The length of your straps is also important if you are playing standing up.
3) If you are a total beginner, it is natural to adopt awkward positions while trying to perform chords. This is a matter of muscular memory which is still to be formed. But when you say "I cant help playing this way because of force of habit", i guess that some sort of adaptation has already taken place. How long have you been practicing?
4) In this specific case, you are using two consecutive fingers in order to press two string which are very far (the first and the last). This is the most strange aspect and, as far as I can tell, playing this chord would not cause any bending of the fingers if done differently (As soon as I go home I'll try on my guitar how I'd play this strange chord... F#min11(b6,b9)? EDIT: I use my index finger on the low E string and my pinky on the high E)
So, my final verdict (edited):
The fact that your fingers appear to be able to bend like that is not a big deal per se, but as some of the other contributors pointed out, doing that can lead to injuries, i guess it is something which is better to avoid. In general, to avoid long term problems watch your whole body position, and always keep an eye on your wrists! Try to figure out which finger combination better works for a specific chord and for your body.
