This paper uses publicly available data and various statistical models to estimate the basic reproduction number (R0) and other disease parameters for Ghana’s early COVID-19 pandemic outbreak. We also test the effectiveness of government imposition of public health measures to reduce the risk of transmission and impact of the pandemic, especially in the early phase. R0 is estimated from the statistical model as 3.21 using a 0.147 estimated growth rate [95% C.I.: 0.137–0.157] and a 15-day time to recovery after COVID-19 infection. This estimate of the initial R0 is consistent with others reported in the literature from other parts of Africa, China and Europe. Our results also indicate that COVID-19 transmission reduced consistently in Ghana after the imposition of public health interventions—such as border restrictions, intra-city movement, quarantine and isolation—during the first phase of the pandemic from March to May 2020. However, the time-dependent reproduction number (Rt) beyond mid-May 2020 does not represent the true situation, given that there was not a consistent testing regime in place. This is also confirmed by our Jack-knife bootstrap estimates which show that the positivity rate over-estimates the true incidence rate from mid-May 2020. Given concerns about virus mutations, delays in vaccination and a possible new wave of the pandemic, there is a need for systematic testing of a representative sample of the population to monitor the reproduction number. There is also an urgent need to increase the availability of testing for the general population to enable early detection, isolation and treatment of infected individuals to reduce progression to severe disease and mortality.