During his ongoing visit to India, Vanhanen told YLE that security levels at the Embassy need to be tightened, and that cooperation with local officials is needed to ascertain the identity of those behind the threat.
Vanhanen added that it is hard to understand the possible motives of whoever made the threat.
"Finland has not profiled itself in that area in such a way that would provoke this kind of behaviour", Vanhanen said.
Foreign Minister Ilkka Kanerva says that the terror threat received by the Finnish Embassy applies to diplomatic missions of all countries in Nairobi.
Kanerva, who is touring Serbia, says that Finland has informed all countries that have embassies in Nairobi about the threat.
He added that the Embassy's facilities have been checked, and security at both the Embassy building and the Ambassador's residence has been stepped up.
Finnish Ambassador Heli Sirve said earlier on Wednesday that three e-mail messages were received at the Embassy during the weekend warning of a threat of a terror attack.
The Embassy has been in contact with Kenyan police, who are investigating the origin of the messages. The e-mails are signed by individuals, and not any organisation. They threat was said to come from Ethiopia, and the names of the senders appear to be of Somali origin.
The Finnish Embassy does not believe that the messages would be linked with political unrest. The Embassy has a staff of 13 Finns and more than ten Kenyans.