Investors worried about the impact of the coronavirus on the world economy might soon have to confront another challenge to corporate profits: a strengthening dollar.

The U.S. currency has climbed steadily since the number of coronavirus cases began surging in China last month, pushing the WSJ Dollar Index to its highest level since early October. With many analysts concerned that disruptions to the Chinese economy will dent global growth, investors have been clinging to U.S. assets, helping the S&P 500 rebound from its...