"Andone cited family reasons for his decision," CSKA's chief executive Ventsislav Zhivkov told a news conference at the club's training ground in Pancharevo.
"He came here with big ambitions but unfortunately he won't be able to fulfil it. We parted as friends and we wish him well in the future."
Former Dinamo Bucharest coach Andone, capped 55 times by his country as a player, replaced crowd favourite Luboslav Penev during the Bulgarian league's winter break in January, signing an 18-month contract.
Penev resigned after failing to guarantee he could deliver the league title this season but the 50-year-old Andone, who won a Romanian domestic double with CFR Cluj in 2008, struggled to inspire the team.
Andone, who was sacked by United Arab Emirates club Al Ahli last November, guided CSKA to only two wins in six matches since the championship resumed with The Reds failing to score in three of them.
A goalless draw with bitter rivals Levski Sofia in the "eternal derby" on Saturday left CSKA third in the standings, eight points behind leaders Litex Lovech after 21 matches.
Andone's departure is another setback for the 31-times Bulgarian champions, who are serving a three-match home ban because of crowd trouble.
Andone's assistant Adalbert Zafirov will take over on an interim basis. CSKA visit Beroe Stara Zagora on Wednesday in the Bulgarian Cup quarter-finals.
"It's a big chance for me," former CSKA and Arminia Bielefeld defender Zafirov said. "Now I'll have the opportunity to prove my abilities."
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