The seven cases were all from al-Ahsa governorate in the east of the country, the Saudi news agency SPA said citing health officials.
The novel coronavirus (NCoV) is a cousin of SARS that causes pneumonia and sometimes kidney failure.
It is from the same family of viruses as the one that caused an outbreak of Severe Acute Respiratory Syndrome (Sars) that emerged in Asia in 2003.
In the statement released by SPA, the Saudi health ministry said it was taking "all precautionary measures for persons who have been in contact with the infected people... and has taken samples from them to examine if they are infected".
However, the ministry gave no details on how many people had been tested for the disease.
In March, WHO said it had been informed of 17 confirmed cases of NCoV worldwide, including 11 deaths.
Cases have been detected in Saudi Arabia, Jordan, Germany and the UK.
Correspondents say the exact source of the new virus and how it spreads are still unknown. One theory is that it comes from animals.
The threat to the general population is thought to be small, although the virus has shown signs of spreading in people.
According to WHO, the last known death from NCoV was a 73-year-old man from the United Arab Emirates, in March.
In February, a patient died in a hospital in Birmingham, England, after three members of the same family became infected.
Back in 2002-2003 some 800 people died of SARS, which comes from the same family as novel coronavirus.