The east African country confirmed its first case of coronavirus on Saturday, becoming one of at least 26 countries on the African continent where the outbreak has spread.
The ministry said in a statement the four additional cases included a 34-year-old man who arrived from South Sudan on March 6 and his brother, who also had a recent history of travel.
A fourth person was a 22-year-old man of Ugandan nationality who arrived in Rwanda from London on Sunday.
The case of the man with no history of travel testing positive would suggest transmission within the community.
Several African governments have closed borders, canceled flights and imposed strict entry and quarantine requirements to try to contain the spread of the outbreak.