In a statement, the government said shark sightings were reported in the Grafton area and the Buccoo Reef Marine Park.
Officials said the closures will allow the coastguard and Department of Fisheries to investigate the incident and “neutralise the shark threat, if possible”.
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December 2023: Why shark sightings are on the rise
A Foreign Office spokesperson said: “We are supporting the family of an injured British man in Tobago and are in contact with the local authorities.”
Last year, there were 69 unprovoked attacks and 22 provoked bites worldwide, along with 14 fatalities, according to the Florida-based International Shark Attack File.