The importance of entrepreneurship growth around the globe has been well recognized and documented by many scholars. For instance, some scholars have reported that the potential contribution of entrepreneurship growth to employment and income has been generally recognized. Entrepreneurs are widely recognized as the prime movers of economic development; the people who translate ideas into action. The government of Kenya has initiated numerous programs and policies to support entrepreneurship growth in Kenya. For instance, it has undertaken policy reviews that have led to reduction of the required licenses to start and operate a business. It has initiated several monetary funds to assist entrepreneurs, particularly youth and women, obtain financing for their enterprises i.e. the Youth Enterprise Fund, Women Enterprise Fund and Uwezo Fund. Private sector players such as commercial Banks, Non-Governmental Organizations (NGOs), Microfinance Institutions (MFIs) and Savings and Credit Co-operatives Societies (SACCOs) among others have also come up with formal financial support schemes for entrepreneurs. However the start- up failure rate is still very high and the desired growth levels are yet to be achieved. Consequently some scholars and policy makers have turned to business incubators and particularly university based business incubators as a possible boost to entrepreneurship growth through nurturing start-ups. A major area in the operation of an incubator is the selection criteria used to admit incubatees. This study aimed to find out the role of selection criteria into university based business incubators on entrepreneurship growth in Kenya. The six active university based business incubators in Kenya were investigated with a specific focus on all the fifty nine graduated incubatees from the said incubators. Census technique was used given that the total number of all graduated incubatees (59) could be adequately studied. The study used a semi structured questionnaire as the main tool of data collection. A combination of tools was used to analyze the data because whereas some aspects of the study were qualitative others were of a quantitative nature. Quantitative data was analyzed using Statistical Package for Social Sciences (SPSS) Version 21 software through descriptive statistics; measures of central tendency (mean and mode), measures of dispersion (standard deviation and variance) and inferential statistics. Thematic analysis was used for qualitative data. The study found out that the kind of selection criteria used by a university based business incubator has a significance impact (79.6%) on entrepreneurship growth. The study recommends among others, that the government through the Ministry of Education, and management of individual universities set up more university based business incubators given the positive potential effect they have on entrepreneurship growth. University based business incubators should continuously enrich their selection criteria in order to attract and incubate only the very potential incubatees. Further studies could be conducted on the role of selection criteria into other kinds business incubators – those not based in universities- on entrepreneurship growth