After the start of the COVID-19 pandemic and its spread across the world, countries have adopted containment measures to stop its transmission, limit fatalities, and relieve hospitals from straining and overwhelming conditions imposed by the virus. Many countries implemented social distancing and lockdown strategies that negatively impacted their economies and the psychological wellbeing of their citizens, even though they contributed to saving lives. Recently approved and available, COVID-19 vaccines can provide a really viable and sustainable option for controlling the pandemic. However, their uptake represents a global challenge due to vaccine hesitancy and logistic–organizational hurdles that have made its distribution stagnant in several developed countries despite several appeals by the media, policy- and decision-makers, and community leaders. Vaccine distribution is also a concern in developing countries, where there is a scarcity of doses. The objective of the present study was to set up a metric to assess vaccination uptake and identify national socio-economic factors influencing this indicator. We conducted a cross-country study. We first estimated the vaccination uptake rate across countries by fitting a logistic model to reported daily case numbers. Using the uptake rate, we estimated the vaccine roll-out index. Next, we used Random Forest, an “off-the-shelf” machine learning algorithm, to study the association between vaccination uptake rate and socio-economic factors. We found that the mean vaccine roll-out index is 0.016 (standard deviation 0.016), with a range between 0.0001 (Haiti) and 0.0829 (Mongolia). The top four factors associated with the vaccine roll-out index are the median per capita income, human development index, percentage of individuals who have used the internet in the last three months, and health expenditure per capita. The still-ongoing COVID-19 pandemic has shed light on the disparity in vaccine adoption across low- and high-income countries, which represents a global public health challenge. We must pave the way for universal access to vaccines and other approved treatments, regardless of demographic structures and underlying health conditions. Income disparity remains, instead, an important cause of vaccine inequity, which restricts the functioning of the global vaccine allocation framework and, thus, the ending of the pandemic. Stronger mechanisms are needed to foster countries’ political willingness to promote vaccine and drug access equity in a globalized society where future pandemics and other global health crises can be anticipated.