In this study, we examine the asymmetric efficiency of cryptocurrencies using 1-hour data of Bitcoin, Ethereum, Litecoin, and Ripple. In doing so, we utilize the asymmetric multifractal detrended fluctuation analysis (MF-DFA). We find significant asymmetric multifractality in the price of cryptocurrencies and that upward trends exhibit stronger multifractality than downward trends. Using the time-varying deficiency measure, we show that the COVID-19 outbreak adversely affected the efficiency of the four cryptocurrencies, given a substantial increase in the levels of inefficiency during the COVID-19 period. Bitcoin and Ethereum are the hardest hit, and at the same time, these two largest cryptocurrencies recovered faster at the end of March 2020 from their sharp dip towards inefficiency. The findings confirm previous evidence that market efficiency is time varying; also, unprecedented catastrophic events, such as the COVID-19 outbreak, have adverse effects of on the efficiency of leading cryptocurrencies.