Reports say the outbreak did not meet the criteria for declaring it a "public health event of worldwide concern", which would trigger the formation of an emergency WHO committee.
The senate has asked Isaac Adewole, minister of health, to get emergency vaccines in the event of a case of Ebola in the country.
Health workers have recorded two confirmed cases, 22 probable cases and 17 suspected cases of Ebola in three health zones of Congo's Equateur province, and identified 432 people who may have had contact with the disease.
The Ministry's spokesperson Jessica Ilunga said this on Tuesday.
"The most important thing is to stop the spread of the disease, and to that end, what they have to do is track down everybody - people who have contracted Ebola or even died from Ebola", CBS News foreign correspondent Debora Patta reports. "The remaining 12 cases are suspected..."
The vaccine, developed by Merck in 2016, has proven safe and effective in human trials, but it is still experimental as it does not yet have a license.
Presenting her motion, Senator Tinubu recalled that an infected immigrant, Mr Patrick Sawyer, who arrived Nigeria on July 23, 2014, was notable for being the index case for the introduction of Ebola virus into Nigeria.
The upper chamber of the National Assembly also called for screening of passengers at the ports, adding that health institutions should be put on red alert because of the Ebola outbreak in the Democratic Republic of Congo.
It will be reserved for people suspected of coming in contact with the disease.
"The senate is be reminded that the tide was stemmed by quick response of the Nigerian government vid declaration of emergency, collaboration of federal and states ministries of health, use of incidence management approach, identification and follow up contacts". "So it means this first shipment would be probably enough for around 25-26 rings - each around one confirmed case".
The cases were reported from Bikoro, Iboko and Wangata, and 393 contacts have been identified so far and are being followed up, the World Health Organization also said.