Ukraine army soldier
In fact not just suicides, the entire non-combat losses of Kiev's army in the war are staggering.

Since the start of the war in east Ukraine up to 1,000 Ukrainian soldiers, veterans and draftees have killed themselves. This is a staggering number considering that by official figures in the entire war 2,275 Ukrainian soldiers were killed in action.

For every two or three soldiers killed by enemy action another soldier, veteran or conscript has taken his own life.

As cited by Interior Minister Avakov in a recent article the Ukrainian Military Prosecutor's office has documented 500 suicides of veterans who had returned from the war in Donbass on Kiev's side.

In addition to that, according to official data 259 soldiers committed suicide on active duty from the start of the war through 2016.

Also there have been many cases of draftees killing themselves rather than be conscripted:
In June 2015, a 43-year-old conscript jumped from a fifth-floor window of Lviv hospital. He was set to undergo a medical evaluation the next day, but, knowing he would be drafted into the army regardless of the results, he preferred to die. The same year, in the town of Zolochiv, a conscript of the National Guard jumped from the top of a military hospital to his death. A 31-year-old conscript from the city of Dnipro jumped off a Kiev-Uzhgorod high-speed train that was delivering him to the front lines.
Not just the suicide rate, but the entire non-combat losses of the Ukrainian army since the start of the war are mind boggling.

According to Kiev's own data since the beginning of the war 121 of its soldiers were murdered (presumably mainly by fellow soldiers), 96 died of drugs and alcohol, 111 due to reckless handling of weapons, 40 due to violation of safety procedures (wandering onto mine fields or being shot by sentries—possibly when drunk), 112 in road accidents (how many were drunk driving?), 148 in other accidents, and 405 due to illnesses.

These numbers give a picture of a force that is completely demoralized and out of control. Murder, suicide, alcohol abuse, depression, aggression, recklessness...

Perhaps the most shocking number is the 405 deaths due to illnesses. What are the sanitary conditions in Ukrainian army barracks? Is this a pre-modern army?

Actually the number is so high that some Ukrainians suspect the military is over reporting deaths due to disease to conceal the extent of suicides and other causes of deaths:
On his Facebook page, Ukrainian journalist Oliksii Bratushchak expressed the anger of his fellow Ukrainians when comparing official figures for combat and non-combat casualties in the Ukrainian army in 2016.

According to the Ukrainian Ministry of Defense's official response to Bratushchak, the combat losses of the Ukrainian army last year were 211 people, while non-combat ones comprised a shocking 256 cases: 63 suicides, 30 murders, 18 deaths due to road accidents, 10 due to drug and alcohol poisoning, 39 due to careless handling of weapons, four due to violations of security procedures, 58 due to illnesses, 29 due to accidents, and five died of other causes.

The real number of suicides in 2016 is most likely higher, since, as Bratushchak pointed out, how could it have happened that 58 people with fatal diseases were sent to the war zone.
In sum, with 1,294 non-combat deaths through 2016, an additional 500 veteran suicides, and many by draftees, it seems the Ukrainian army is as great a menace to its soldiers as the Donbass rebels.