They have put up wanted posters in hostels around the town, which is hosting the Winter Olympics next month.
The 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.
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 December 29 and 30.
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 February 7. Washington has also offered to supply Russia with hi-tech equipment to help detect improvised explosives.
ysKX1ggSrxgAt least five people, including a four-month-old baby, have been killed after dozens of tornadoes…
Harvey Weinstein has been hospitalized just days after his 2020 rape conviction in New York…
Hamas has published a video showing the first proof of life of US and Israeli…
Prosecutors and Donald Trump’s attorneys delivered opening statements and the first witness was called on…
The House of Representatives has finally approved $61 billion in new US military aid for…
The real estate market in the United States has always been a gauge for economic…