Vapaavuori received support from a quarter of the party's council representatives followed by Petteri Orpo with 18%.
The third most popular candidate was Paula Risikko, the social affairs and health minister, with 15% of the support while fourth was Alexander Stubb, the foreign trade minister, with 14%.
Henna Virkkunen, the minister of transport and local government, received 7% of the support.
The survey was answered by 102 the party's district representatives. As many as 14% do not yet know or could not tell who their preferred candidate was.
The next leader of the party will be elected in June. No one has officially announced his candidature.