The case marks the first time a new country has been hit by the outbreak since July and comes a day after the World Health Organisation warned the number of infections is increasing rapidly yesterday.
Senegal's health ministry said the patient is a young Guinean man who was immediately quarantined at a Dakar hospital, where he is in a "satisfactory condition".
The man is believed to have been infected in Guinea's capital Conakry, and may have travelled to Senegal before Dakar closed its land border with Guinea on August 21.
New figures released by the WHO on Thursday revealed the massive scale of the crisis, which it said indicated a "rapid increase still in the intensity of transmission" that could cost at least USD 490 million to tackle.
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In a sign that affected countries are struggling to stop its spread, the UN agency said the number of cases could exceed 20,000 before the epidemic is brought under control.
Never before has there been an Ebola outbreak so large, nor has the virus - which was first detected in 1976 - ever infected people in West Africa until now.
Liberia was the worst affected with 694 deaths; 422 people have died in Sierra Leone; and 430 in Guinea, where the virus emerged at the start of the year. Nigeria has now recorded six deaths.
The Democratic Republic of Congo has also confirmed two cases of Ebola, but officials there insist it is unconnected to the current outbreak in West Africa.
Nigeria's latest death - in the southeastern oil city of Port Harcourt - was the first outside its biggest city, Lagos, and dashed hopes that the country had successfully contained the virus.
Some 160 people are now under surveillance in Port Harcourt following the doctor's death, the local government said yesterday.