According to the Centres for Disease Control and Prevention (CDC), the World Health Organisation (WHO) and the NHS, there is no evidence to suggest the virus can be spread by perspiration/sweat.
The NHS has published an article regarding virus transmission, stating that the two routes of transmission are via respiratory droplets (from sneezing, coughing or speaking) or fomites (objects that become contaminated with infected organisms and which subsequently transmits those organisms to another person. Examples of potential fomites are surfaces, toys, mobile telephones or any inanimate objects). This is why keeping a safe distance and disinfecting hands and surfaces before and after use are so important.
Reference: https://www.england.nhs.uk/coronavirus/primary-care/about-covid-19/virus-transmission/