The British couple, who have not been named, were staying at the Kenyan resort Kiwayu Safari Village close to the border with Somalia when gunmen burst into their beach hut late in the night on Saturday.
The man is believed to have been deadly shot after trying to resist the attackers, who ordered the couple to hand over their valuables.
The woman was dragged to the speedboat on which the gunmen had arrived and has not been seen since.
The British government has called for the release of the kidnapped woman.
The Kenyan refused to speculate on who the attackers might be, but officers feared the raid may have been carried out by members of the Somali Islamist insurgent group al-Shabaab rather than pirates, according to the Guardian.
Nairobi government has sent anti-terror and special crimes officers to the area as part of an enormous search and rescue mission, but, according to Ndegwa Muhoro, director of the country’s criminal investigation department, no sign had been received from the woman’s abductors so far.
“We believe it is a kidnap but we are yet to receive any communication from the alleged kidnappers, over 11 hours after they took her with them,” Ndegwa Muhoro said.
A Foreign and Commonwealth Office (FCO) spokesman said:
“We can confirm that two British citizens were attacked overnight at a beach resort north of Lamu, near the Kenya-Somalia border.
“One was killed and another kidnapped. We are working closely with the Kenyan authorities to establish further details.”
FCO did not release the names of the couple for fear of further endangering the woman, but said it is doing all it can to effect her release.
“We have deployed a consular team from our high commission in Nairobi and are offering all possible support to the family of those involved,” FCO spokesman said.
“Our thoughts are with them at this difficult time.
“We are working to secure the safe and swift release of the British national who has been kidnapped and ask those involved to show compassion and release the individual immediately.”
Two nuns from Western Europe were kidnapped in November 2008 and three aid workers were abducted in July 2009.
Accordind to Police Commissioner Mathew Iteere said the couple had come from a trip to the Masai Mara reserve and were the resort’s only guests.
Attacks on tourists are unusual in Kenya, which is popular for its safari vacations and pristine beaches.
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