No. But they need an Estonian address.
Nevertheless, all sole proprietors (FIE) must file an application to be entered into the commercial register before they start operating. Individuals from creative professions working on a freelance basis are subject to the same requirement.
There is no need to register separately with the Estonian Tax and Customs Board, as the information about registration will be forwarded automatically.
If an e-resident registers as a sole proprietor in Estonia, it is accompanied by a commitment to pay advance payments of social tax 4 times a year. The size of advance payment actually does not depend on the size of income, it is set each year with the state budget.