"Today the club made a decision to part company with the head coach," the outfit, bankrolled by billionaire Suleiman Kerimov (pictured), said on their website.
Krasnozhan, 48, joined Anzhi at the end of the year after he was sacked by Lokomotiv Moscow earlier in the season despite them being among the league leaders at the time. Lokomotiv said he was fired for "negligence in his job" following a controversial defeat by Anzhi.
"I can only say that the main reason for my departure was the difference in the main principles of directing the team," Krasnozhan said in a brief statement, posted on the club's website.
Local media, however, said the true reason for the sacking was Krasnozhan's inability to deal with Anzhi's biggest names - Cameroon striker Samuel Eto'o and Brazilian full-back Roberto Carlos.
Media reports also made Fabio Capello the favourite to take the hot seat. Reports said the Italian, who quit as England manager last week, visited Moscow at the weekend to negotiate a deal with Anzhi.
Krasnozhan's departure had been widely expected since general director Alan Soziyev, Krasnozhan's former agent, was fired by Anzhi over the weekend.
Shortly after taking the job in December, Soziyev brought Krasnozhan to the wealthy club from the volatile North Caucasus region to replace Andrei Gordeyev and Roberto Carlos.
The duo had been placed in charge in a joint-caretaker capacity in September when long-serving coach Gadzhi Gadzhiyev was sacked.
Kerimov's money helped to lure Eto'o from Inter Milan last year. According to media reports, the four-times African Footballer of the Year, who signed a three-year deal in August, is now the highest-paid player in world football with an annual salary of 20 million euros.
