"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.
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."
