The death has sparked public health fears on social media, but authorities on Monday said the situation was under control.
The World Health Organisation said based on available information, "the public health risk to the general population appears to be low".
New risk assessments would be conducted once further information became known, it said.
US President Donald Trump said the death was a "big problem for Russia" and offered to help Moscow deal with it.
"We'll help," Trump said.
"Anybody that has that kind of a problem, we're always willing to help."
US Secretary of State Marco Rubio said Washington was closely monitoring the situation.
Plague is endemic to Siberia, location of the first known prehistoric human outbreak, as the bacterium that causes it, Yersinia pestis, is present among the small wild mammals in its vast wilderness and their fleas. It is rare for Russians to fall ill with plague, however, though cases occur every year in other parts of the world — notably Africa.
Plague comes in three forms affecting different parts of the body. Pneumonic plague, an infection of the lungs, prompts the patient to cough out infectious airborne droplets.
If identified quickly, it can be treated with antibiotics. But if left untreated, it can be fatal in one to six days.
Local media have named the laboratory worker who died as Darya Shipilova, a 28-year-old employee at the Irkutsk Anti-Plague Research Institute of Siberia and the Far East.
There were conflicting reports about how and where she fell ill, but the authorities said she had died of pneumonia of as-yet unestablished origin.
Russia's health watchdog, Rospotrebnadzor, told state media the institute had not found evidence of any accidents involving the handling of pathogens after rumours spread on social media that the woman had dropped a test tube containing live bacteria.
Nevertheless, Anna Popova, the head of Rospotrebnadzor, flew to Siberia for an emergency meeting over the weekend.
According to Russian media reports, about 200 people who had been in contact with the dead woman were quarantined, parts of the hospital in the town of Shelekhov where she died were cordoned off and an aluminium plant told its workers to wear masks.
Rospotrebnadzor, in a later statement quoted by the TASS news agency, said officials in Irkutsk Region had found two cases of COVID and two cases of rhinoviruses among people who had been in contact with her. No other cases of infectious diseases were noted.
Authorities urged people to remain calm and said there was no evidence the woman's death was linked to her work.
Igor Kobzev, the governor of the Irkutsk region, said in a statement that she had died of "pneumonia of unknown aetiology", adding: "Importantly, over the past few days, no new cases of staff from the Anti-Plague Institute seeking medical attention have been identified."
He said the situation was under control and that all known contacts of the dead woman had been identified, examined and placed under medical supervision.
