All pupils in the class have been asked to stay at home, get tested, isolate, and follow the guidelines given in an email that was sent to households.
The school and all other classes remain open and children can attend as normal.
Parents and families are asked to only come onto the school grounds if necessary.
Carlton principal Gary Johnson said the Ministry of Education had support coordinators liaising with both himself and the Ministry of Health.
"They are working us through it, and while it's not quite business as usual, we are operating and we are being really aware of all our health and safety measures," Johnson said.
"Fortunately, we have planned well for this and we've got really good support."
The pupils had come to school on Monday in "a pretty good space", Johnson said.
"For me, it's important to keep everyone calm, informed of what's going on, and checking everyone's health and safety, as well as their emotional and mental wellbeing.
"That's probably going to be as big a factor as anything else.
"I've got fantastic staff here. The field changes all the time, but they're adapting. They're calm in class and our tamariki are picking that up and carrying on."
Principals at other local schools had been in contact with him following the school's announcement, Johnson said.
"They're checking if things are ok, and checking on my own wellbeing as well.
"It really is a time of people pulling together, which is great."
Close contact location revealed
The Subway at the upper end of Victoria Ave was named as a high-risk location of interest by the Ministry of Health.
All those at the Subway at 396 Victoria Ave, opposite Pak'nSave, between 7pm and 7.30pm on Thursday, February 17, should self-isolate for seven days, and test on day five after they were exposed.
"You should monitor symptoms for 10 days and test again if you feel unwell," the ministry says.
People who were there should record their visit online or call Healthline so that contact tracers can get in touch.
The Whanganui District Health Board said the CBAC (Community Based Assessment Centre) at Whanganui Hospital administered 100 Covid-19 tests on Saturday and 143 on Sunday.
There were 50 tests administered in Marton on Sunday.
In total, 2365 new community cases of Covid-19 were recorded in New Zealand yesterday.
