The attack happened in the waters off the Anse Lazio beach on the island of Praslin.
30-year-old Ian Redmond, who was on honeymoon with his new wife, Gemma, was swimming just 20 metres from the beach. His wife of eleven days was sunbathing when she heard his screams.
"We heard screaming and people started running down the beach towards the water," an American tourist told Britain's Daily Mail. "Someone had seen a fin sticking out of the water, and then we saw a dinghy pulling a man from the water."
"At this point a woman ran over and started screaming. She said "that's my husband. We were just married."
Mr Redmond was helped by a French doctor who was holidaying on the island but he is believed to have died moments after the attack.
The shocking incident comes just two weeks after a 36-year-old French tourist died in similar conditions while snorkelling off the same beach on at the start of August.
Nicolas Virolle, a teacher from Rodez in the south west of the country, was killed by a shark on the last day of his holiday while swimming just 30 metres from the shore.
A temporary ban on swimming or entering the waters around parts of Praslin has been ordered and authorities are reported to have asked shark experts from South Africa to help them identify the creature.
Until now, shark attacks in the Seychelles have been very rare. The last recorded attack before this month's incidents was in 1963.