The study investigates the safe haven properties and sustainability of the top five cryptocurrencies (Bitcoin, Ethereum, Dash, Monero, and Ripple) and gold for BRICS stock markets during the COVID-19 crisis period from 31 January 2020 to 17 September 2020 in comparison to the precrisis period from 1 January 2016 to 30 January 2020, in a nonlinear and asymmetric framework using Nonlinear Autoregressive Distributed Lag (NARDL) methodology. Our results show that the relationship dynamics of stock market and cryptocurrency returns both in the short and long run are changing during the COVID-19 crisis period, which justifies our study using the nonlinear and asymmetric model. As far as a sustainable safe haven is concerned, Dash and Ripple are found to be a safe haven for all the five markets before the pandemic. However, all five cryptocurrencies are found to be a safe haven for three emerging markets, such as Brazil, China, and Russia, during the financial crisis. In a comparative framework, gold is found to be a suitable safe haven only for Brazil and Russia. The results have implications for index fund managers of BRICS markets to include Dash and Ripple in their portfolio as safe haven assets to protect its value during a stock market crisis.