Irma -- which has killed at least 19 people and devastated thousands of homes in the Caribbean -- made landfall late yesterday on the Camaguey Archipelago of Cuba.
"Hurricane Irma -- Our missions in Caracas (Venezuela's capital), Havana (Cuba's capital), Georgetown (Cayman Islands) and Port of Spain (Trinidad and Tobago) have reported that all Indian nationals there are safe," Swaraj tweeted.
Earlier, the External Affairs Ministry said that it was monitoring the situation and communicating with the Indian diaspora in the US, Venezuela, France and the Netherlands in the wake of deadly hurricane Irma.
"Our missions in Venezuela, the Netherlands, France and the US are constantly monitoring the situation following destruction due to hurricane Irma. They are in constant touch with the Indian diaspora affected by Irma and with local government officials to provide all possible assistance," Kumar said in a series of tweets.
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Irma was barrelling towards Florida after making landfall in Cuba's Camaguey Archipelago.
France said at least 10 people have been killed across its Caribbean territories with seven more missing. Two people died on the Dutch side of the Saint Martin island.
The Indian Embassy in the Netherlands tweeted that they were in touch with the Dutch government.
The Indian embassy in Caracas in Venezuela was also monitoring the situation in Saint Martin and "coordinating the welfare of all Indians living there.