The incident occurred on Tuesday evening as the 22-year-old woman was celebrating her birthday with colleagues at the office where she worked.
The 23-year-old man, who has not yet been named, reportedly went on an extended drinking spree after his live-in-lover told him she was leaving him. He subsequently entered her place of employment, tracked her down and put a knife to her throat.
He initially demanded a car and 50,000 rubles ($2,000). However, he then changed his mind and asked for a gun, saying that he wanted to kill himself and his former girlfriend.
"He was shot just as the weapon was being passed to him," the spokesperson said, adding that police had spent half an hour trying to persuade him to release his hostage.
The young man died at the scene. There were no other casualties.
The woman, whose identity has also not been revealed, is currently undergoing treatment for shock.