Krasnozhan's sacking came as a shock to most soccer experts after he had led modest Kuban to fourth place midway through the season - their best position in Russia's top flight.
"It was a tough decision but we have agreed to end our collaboration with Yuri Krasnozhan," Kuban's chief investor Oleg Mkrtchan told the club's website
"The opinions of our sporting director and the head coach have become incompatible. The club is much more than just a line in the standings. We have strategic goals, and in this case, they're much more important than a place in the table."
Krasnozhan, 49, was appointed Kuban coach in August when he replaced former Romania and Chelsea defender Dan Petrescu, who left to coach fellow Russian Premier League club Dynamo Moscow.
Krasnozhan has now been sacked by three Premier League clubs in the past 18 months for reasons other than on-field performances.
He was hired by Lokomotiv Moscow before the 2011 campaign after guiding unfashionable Spartak Nalchik to a respectable sixth-place finish the previous season but they fired him a few months later despite being among the leaders at the time.
Lokomotiv said he was fired for "negligence in his job" following a controversial defeat by Anzhi Makhachkala.
Last December, Krasnozhan was named Anzhi coach but this time he lasted only five weeks before being sacked by the wealthy club from the volatile North Caucasus region.
Kuban said they would soon name Krasnozhan's successor, with Belarussian coach Leonid Kuchuk considered the favourite for the hot seat.