Uganda's first case was announced early on Sunday by Health Minister Jane Ruth Aceng. She said the man flew into the country from Dubai on Saturday and was in stable condition.
More than 1000 cases have now been reported across Africa,according to the World Health Organisation.
There are concerns that the continent will not be able to handle a surge in cases without the depth of medical facilities available in more developed economies.
Zimbabwe reported its first case on Friday,and a second on Saturday,while the island of Mauritius,with 14 cases,reported its first death,a person who had travelled from Belgium via Dubai.
Many African countries have already shut their borders,closed schools and universities and barred large public gatherings.
In South Africa,which has the most cases in sub-Saharan Africa,more citizens have taken to wearing masks and gloves in public as the number of confirmed cases rose on Saturday to 240.