The eruption column was estimated to have reached 10 kilometres high, the University of the West Indies Seismic Research Centre said, warning other explosive eruptions could occur.
He added that in the event there are more explosive eruptions, it would still be the communities in the red zone that would get the brunt of it.
Joseph said it was impossible to predict whether any potential upcoming explosions would be bigger or smaller than the first one.
Authorities on the island have reported no casualties so far; St Vincent has seen a number of fatal volcanic eruptions in the past.
The prime minister at an emergency news conference said that no evacuation order has been given but persons are wanted to be prepared to evacuate at short notice.
The prime minister acknowledged then the challenges of conducting emergency operations during the pandemic but said that strict health protocols - like the obligatory use of masks and social distancing where possible - would be in place during evacuations and in shelters.
He said that Barbados and St. Lucia are willing to receive evacuees, but they will have to be vaccinated against COVID-19.
'Not everything is going to go ideal, but if we all cooperate. we will come through this stronger than ever, ' Gonsalves said.
'This is an emergency situation, and everybody understands that, ' he said.
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"Of course, large numbers of persons still would have to stay in the shelters but the more we get persons who can go into homes and who can go into the hotels and the guest houses, whether here or outside of St Vincent and the Grenadines, we should do so".
By late Thursday evening, shelters were filling up as a string of vehicle lights making their way to safer ground twinkled through the darkened mountains.
Officials tweeted that the dome of the volcano in the island's northern region could be seen glowing overnight.
The alert issued on Wednesday follows days of seismic activity around La Soufriere.
Gonsalves urged people to remain calm and orderly.
"I don't want you panicked", he instructed. 'That is the worst thing to do'.
No further warning is expected, Robertson added, while advising the prime minister to take action to safeguard life and limb.
However, Robertson said no one can say exactly when that would happen.
[Updated] The Premier has extended his thoughts and prayers to the people of St. Vincent & The Grenadines as they face the possible eruption of the volcano La Soufriere.
Gonsalves indicated that other Caribbean countries, including Trinidad and Tobago, Guyana and St Kitts and Nevis have also offered support.