They said the accident happened late on Monday in an area where the army is fighting pro-Russian separatists.
Authorities have urgently appealed for blood donations to treat the wounded.
Local media reports said that those killed in the bus crash were members of the National Guard.
"During a rotation of volunteers and servicemen in the area of anti-terrorist operations on January 5, military trucks and a bus collided in bad weather conditions," a police statement said.
No other details of the accident were released.
Sporadic shelling between Ukrainian forces and separatists in the east has been reported despite a ceasefire.
Ukraine and the West accuse Russia of sending heavy weapons and troops to help separatists in eastern Ukraine following the overthrow of pro-Russian President Viktor Yanukovych in February 2014.
Nearly 5,000 people have been killed in the conflict, which has also led to a deterioration in relations between Russia and the West.
Russia admits that "volunteers" have gone to the east, but denies boosting the rebel ranks with regular troops and hi-tech equipment.
It accuses the Ukrainian government of indiscriminate shooting in a "punitive" military campaign there.
Source: BBC News Europe