Singapore must be prepared for the number of people in the country infected with the new coronavirus disease — formally named COVID-19 — to continue to climb in the coming weeks, a minister said on Friday.

As of Thursday noon, Singapore had 58 confirmed cases of COVID-19, 15 of which have recovered and been discharged, according to the country's Ministry of Health. The Southeast Asian nation with a population of 5.7 million has one of the highest numbers of cases outside China.

Singapore has not recorded any deaths, but that too is something people must be "psychologically prepared" for as the number of cases continues to rise, said Janil Puthucheary, senior minister of state at Singapore's Ministry of Transport and Ministry of Communications and Information.

"I think it's really too early to talk about a peak. Cases are coming in on a daily basis and you have to have the expectation there are going to be more cases over the next few weeks," he told CNBC's "Squawk Box Asia."