The increasing globalization in banking and financial services along with use of cryptocurrencies as a medium of exchange and means of payments, is creating monetary policy uncertainty and concerns in the monetary policy process of central banks, especially difficulty in knowing exactly how much money people are willing to hold at any given point in time, how best to correctly measure the assets that constitutes money and determines the demand for money in the economy. Classical economic theory tells us that, there is a direct relationship between the quantity of money in an economy and the general level of domestic prices. This has made many central banks to adopt monetary aggregates as intermediate targets, in their quest to maintain price stability and achieve sustainable economic growth and development. This study seek to estimate the demand for money function in Nigeria during the period 1980 to 2019 with a view to ascertaining whether monetary policy uncertainty is an important determent of money demand in Nigeria or not. We employed the autoregressive distributed lag (ARDL) to model the relationship between money demand and its determinants using times series data from 1980 to 2019. The results indicated that monetary policy uncertainty (MUC) appear to have little or no influence on the demand for money in Nigeria, compared to real income, the nominal exchange rate and domestic inflation. The results confirm that Monetary policy uncertainty (MUC) was not an important determinant of the demand for money in Nigeria during the period 1980 to 2019. It agrees with the findings of El-Rasheed et al., (2017) but disagrees with those of Iyke and Sin-YU Ho (2017) who in a similar study on Ghana, found monetary policy uncertainty to be insignificant in determining the demand for money in Ghana. We therefore bring into focus the need for policy makers in Nigeria and other developing economies to consider monetary policy uncertainty in their monetary policy formulation process because of its positive relationship with how much money Nigerians demand or hold at any given point in time. In addition, this study also found a link between money demand and changes in rate of inflation, nominal and real effective exchange rates and rate of growth in real GDP or real income. The sign and size of the estimated parameter coefficients had the correct a priori expectations, with inflation, monetary policy uncertainty and real GDP growth rates having a positive relationship with money demand, while the exchange rate responding negatively. There is need for more studies using other methods to further confirm this result, especially with respect to its application to other developing economies that may not be an oil exporting, import dependent economy like Nigeria.