The new cases include two Kuwaiti nationals who travelled to Saudi Arabia, two Kuwaiti nationals who travelled to Egypt, and one Kuwait national who travelled to France.
Out of the 13 cases, two cases include Kuwaitis who were in contact with a previously confirmed case who had been to Saudi Arabia.
Another two cases are of a Kuwaiti national and a resident who had been in direct contact with a traveller who went to Azerbaijan.
One case also involves a Kuwaiti national who was in contact with someone who had been to the United Kingdom, while one Kuwaiti national is currently under epidemic investigation.
A spokesman said that an Egyptian resident who was in contact with a previously infected Filipino resident has also been infected with the virus.
The final new case involves a Somalian resident who was in contact with a previously infected person.
Seven people with coronavirus are currently in intensive care units, the spokesman said. Kuwait had earlier reported that a total of 49 people have recovered from the virus.
Kuwait has taken several precautionary measures to prevent the coronavirus from spreading further.