The global crude oil market has experienced a significant downturn following the novel coronavirus outbreak (COVID-19) in December 2019. Thereafter, all the major oil markets have become extremely volatile, and investments in these markets could lead to substantial losses. This paper empirically investigates the time-varying correlations between gold and oil markets to examine whether gold is a safe haven asset for the international crude oil markets during the COVID-19 period. For the purpose of comparison, the safe haven property of Bitcoin is tested as well. The results of the time-varying correlations obtained through the DCC-GARCH model suggest that gold is a safe haven asset for global crude oil markets. Bitcoin, on the other hand, acts only as a diversifier for crude oil. The results further show that the portfolio risk is minimized when investors include oil and gold in their portfolio rather than holding assets in oil and Bitcoin markets. Given that financial downturn, terrorist attacks, pandemics and similar global events often play a crucial role in portfolio risk analysis, our results could be of interest to those who invest in oil, gold and Bitcoin markets.