A further 12 positive cases of Covid-19 were reported on the island on Sunday night, bringing the total number to 39.
More than 100 people have been told to self isolate, accounting for more than 10 per cent of the island’s population.
Asked about the outbreak at the Coronavirus daily briefing on Monday, Dr Smith said: “What we’re seeing in Barra just now is a good example of what happens when perhaps people let their guard down and come together, and this virus takes every opportunity it can to spread between people.”
NHS Western Isles had said the outbreak is likely to be attributed to locals visiting the mainland and carrying the virus back with them.
Sources on the island have pointed to a number of parties around the festive season, with the suggestion that after some people flouted restrictions believing there to be no cases of Covid-19 on the island.
The outbreak, the first to appear on Barra, was reported on January 13 with three cases.
Two patients have been flown off the island – one to Stornoway and one to the mainland.
The island has entered local shutdown, with schools closed, hospital visiting suspended, mass cancelled and shops operating reduced opening hours, with phone order systems in place.
All those identified as close contacts of the positive cases have been offered Covid-19 testing. The influx of tests has caused pressure on the nearest laboratory, in Stornoway, and some cases have been reported with a slight delay.
An Incident Management Team has been set up, and meetings were held last week and over the weekend.
Dr Smith said the outbreak is being monitored “very closely”.
“The First Minister and I have had some preliminary discussions about it, and we will continue that discussion with ministers and officials over the course of the day,” he said.
"We will then decide how we want to take that forward to try to limit and contain any further spread within those communities."