They have put up wanted posters in hostels around the town, which is hosting the Winter Olympics next month.
The woman, 23-year-old Ruzanna Ibragimova from Dagestan in the North Caucasus region, is believed to be the widow of an Islamist militant.
She is thought to have slipped into Sochi earlier this month, bypassing tight security ahead of the Games.
At least two other potential female suicide bombers are also at large in the region, other police posters state.
Russian President Vladimir Putin has launched one of the biggest security operations in Olympic history, and has personally inspected the sites.
More than 30,000 police and interior ministry troops have been deployed and access to the area limited.
Security fears were heightened after two suicide bomb attacks killed 34 people in the southern city of Volgograd on 29 and 30 December.
US President Barack Obama, in a telephone conversation with the Kremlin on Tuesday, offered America's "full assistance" in making the Olympics "safe and secure", the White House said.
Two US warships will be on standby in the Black Sea when the Games begin on 7 February. Washington has also offered to supply Russia with hi-tech equipment to help detect improvised explosives.
Islamist militants from Dagestan and nearby republics of Ingushetia and Chechnya are considered by Moscow to be a major threat to the Games.
Several national Olympic associations have reported being sent an email threatening athletes with attack, but it was widely dismissed by the International Olympic Committee (IOC) and national bodies as not credible.
The IOC said it appeared to be  "a random message from a member of the public," and posed no threat, but repeated that it "takes security very seriously".
Officials at the British Olympic Association said they "receive correspondence of every type and it is not uncommon to come across something like this that lacks credibility".
"It is extremely important in matters such as this that everyone maintains a level head and a sensible perspective," said spokesman Darryl Seibel.

The Pope said migrants often met "rejection from those who could offer them welcome and assistance".
He also condemned terrorism as "a blind and brutal violence" that should be fought with "weapons of love".
The Pope was delivering his "urbi et orbi" (To the city and the world) message to thousands amid tight security in St Peter's Square.
The Pope said: "The Easter message of the risen Christ... invites us not to forget those men and women seeking a better future, an ever more numerous throng of migrants and refugees... fleeing from war, hunger, poverty and social injustice.
"All too often, these brothers and sisters of ours meet along the way with death or, in any event, rejection by those who could offer them welcome and assistance."
Tens of thousands of migrants, mainly fleeing conflict in Syria and Iraq, are now stranded in Greece, after European nations and Turkey agreed a plan to shut their route to northern Europe.
Pope Francis also offered a prayer for Syria: "The risen Christ points out paths of hope to beloved Syria, a country torn by a lengthy conflict with its sad wake of destruction, death, contempt for humanitarian law and the breakdown of civil concord."
He expressed his hope for success at peace scheduled to resume next month.
The Pope also urged people to use the "weapons of love" to combat the evil of terrorism.
He spoke of recent attacks in Belgium, Turkey, Nigeria, Chad, Cameroon, Ivory Coast, and Iraq.
"May [the risen Jesus Christ] draw us closer on this Easter feast to the victims of terrorism, that blind and brutal form of violence which continues to shed blood in different parts of the world," he said (text in Italian).
The latest terror attack - in Brussels on Tuesday - left 28 people dead. The former king and queen of Belgium, Albert II and Paola, attended the Mass on Sunday and met the Pope.
Many pilgrims cancelled their planned trips to Rome in the wake of the violence in Brussels, but the square was packed on Sunday, as was St Peter's Basilica when Pope Francis celebrated Mass on Saturday evening.
In his homily in the basilica, he called on Christians not to let fear and pessimism "imprison" them.
He said: "Today is the celebration of our hope. It is so necessary today."
Russian police in Sochi are hunting for a woman they fear may be planning to carry out a suicide bomb attack.
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Pope Francis has condemned those who fail to help migrants, during his traditional Easter speech in Rome.