"The Senate is disturbed that recent reports by media outlets and the World Health Organisation show that the disease is back in the neighbouring Democratic Republic of Congo with 19 dead and 39 infected recorded so far".
It said 393 people who identified as contacts of Ebola patients were being followed up.
Vaccinations could begin by next Monday, he said.
The vaccine was developed by the Canadian government and is now licensed to the US -based Merck. It must be kept at -60 to -80 degrees Celsius (-76°F to -112°F), creating huge logistical challenges.
Ebola Outbreak Leads to 19 Deaths in Congo
Tinubu recalled that an infected immigrant, Mr Patrick Sawyer who arrived Nigeria in July 23, 2014 was notable for been the index case for the introduction of Ebola virus into Nigeria.
The worst Ebola outbreak yet started in December 2013 in southern Guinea, before spreading to two neighbouring West African countries, Liberia and Sierra Leone, killing more than 11 300 people out of almost 29 000 registered cases. "If a general can not be with its troops in the front line it's not a general", he said.
After meeting DRC President Joseph Kabila in Kinshasa, the WHO chief praised the government's very strong leadership in responding to the health crisis and its good coordination with partners like Unicef and Doctors without Borders.
Of the 20 people who died in the DRC, three are health workers, said the director, adding that the outbreak has also occurred in a remote part of the country, challenging deployment of health workers and the necessary supplies, which has made the situation a big concern.