The five cases include four citizens, including three who arrived from Iran and Iraq, and an Egyptian, the official Saudi Press Agency reported.
Saudi Arabia has taken a number of precautionary measures to curb the spread of the virus, including the suspension of flights to and from 14 countries.
The countries are the United Arab Emirates (UAE), Egypt, Kuwait, Bahrain, Iraq, Lebanon, Syria, South Korea, Italy, Oman, France, Germany, Turkey and Spain.
It also temporarily suspended study at schools, universities and other educational institutions as of Monday.
The kingdom has also imposed overnight closure of the Grand Mosque in the city of Mecca and the Prophet Mohammed's Mosque in Medina. It also halted Umrah pilgrimages to Mecca.
Kuwait also announced four new confirmed cases over the past 24 hours, raising the total number in the Gulf state to 69.
In Qatar, a total of 18 cases have been detected so far.
Egypt has raised the total number of infections to 59, after four new cases were recorded.
Egypt's Prime Minister Mostafa Madbouli has decided to suspend all activities that involve large gatherings of citizens or those that require the movement of people in large numbers between provinces.
A statement by the prime minister's office late Monday said the move was part of precautionary measures to deal with the virus.