Lukyanova, a law professor at Moscow State University and the daughter of former Supreme Soviet Chairman Anatoly Lukyanov, said she decided in part to leave because she believed the race would be unfair.
"I withdrew because I cannot take part in an election where a candidate does not enjoy the same rights I do," she said, referring to Vladimir Kvachkov, the retired colonel who is in custody on charges of trying to kill Unified Energy Systems chief Anatoly Chubais.
Kvachkov took part in a Duma by-election in Moscow's Preobrazhensky district in December, but he was not allowed to campaign from jail. He also is unlikely to be allowed to place campaign ads on television and radio during this race.
"This is a violation, and as a lawyer I cannot accept it," Lukyanova said by telephone.
The March 12 by-election in the city's northeastern Medvedkovo district was called to fill the seat vacated by Georgy Boos, who became Kaliningrad governor in September.
Lukyanova said another reason she decided to withdraw was that the Duma "has turned into a rubber stamp that only follows orders from above."
She said the Communist Party backed her decision.
More than 20 people are expected to run in the by-election, although only two candidates have filed applications so far: United Russia candidate Leonid Govorov, the head of the Moscow Chamber of Commerce and nephew of Soviet Marshal Leonid Govorov, and Liberal Democratic Party candidate Igor Dyakov, editor of the Puteshestvennik magazine, a district election official said Monday.
The registration deadline is Wednesday.
Kvachkov's lawyer, Alevtin Moshansky, said his client "has more chance of winning the election" now that Lukyanova has pulled out.
Kvachkov, who intends to run as an independent, can take part in the by-election because he has not yet been convicted of any crime.
Lukyanova's bid had the support of an alliance of Communists and some liberals. Garry Kasparov, the chess champion turned liberal politician, had called her and asked whether she would agree to be backed by the liberals. Yabloko, however, has said it would field its own candidate.
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