The policewoman sustained an eye injury and underwent surgery.
"She is still in bad condition," police chief commissioner Anton Zlatanov said. "She underwent surgery but there are many pieces of glass on her face and in the eye.
"Such an act is inadmissible. It's not a firework or a small bomb, it's a bomb. This is an extremely unpleasant and ugly incident."
He said the bomb had been thrown from the Levski fans' section at a door near one of the stadium entrances, adding that another police officer sustained minor injuries.
"More than 20 Levski fans were detained but I can't tell the exact number," Zlatanov said.
The Eternal derby, as matches between the two most popular clubs in the Balkan country are called, ended in a 2-2 draw. CSKA are second in the standings, eight points behind leaders Ludogorets. Levski are fourth.
The fixture has a long history of crowd violence.
A man was killed by a bomb after the game in 2000 and hooliganism and arrests have been rife since then.
(Reporting by Angel Krasimirov, editing by Ed Osmond)
