A record 1,304 cases were reported to UK police forces last year, nearly three times as many as 2015, the agency said.
The scam involves organised criminal gangs using fake online dating profiles to befriend victims, usually young men.
They encourage the target to film themselves performing sex acts and use a pre-recorded video purporting to show them doing the same. The gangs secretly record their victims and then blackmail them, threatening to share the footage with their family and friends unless they pay thousands of pounds.
At least five British men and boys have killed themselves after being targeted.
Many victims are young males aged between 17 and 25, although men aged over 60 are also particularly vulnerable, the NCA said. There has also been a rise in armed forces personnel falling victim to the scam, the agency added.
It warned many cases went unreported and that tens of thousands of men may be targeted each year.
There were 428 cases reported in 2015, the NCA said.
“The upward trend in cases of sextortion and the devastating effect on victims are extremely worrying,” said John Branney, of the agency’s anti-kidnap and extortion unit.
He added: “Due to the nature of the crime we know there are a huge number of cases that go unreported and that the figures released today are just the tip of the iceberg. The release of these figures aims to highlight sextortion as a growing crime and help potential victims by showing them how they can protect themselves and what to do if they are targeted.
“We want victims to know that they are not alone and urge them to contact the police where they will be treated sensitively and in confidence.”
In June 2015, 17-year-old Ronan Hughes from County Tyrone in Northern Ireland took his own life after being tricked into sharing intimate pictures of himself online.
A Romanian gang had posed as a girl called “Emily Magee” and asked him to send the photos, which they then shared with his friends when he was unable to pay a €3,000 (£2,600) ransom.
Hours after the pictures were posted online, Ronan – remembered as a “happy-go-lucky” teenager – killed himself.
An international investigation later traced the people behind the scame to the Romanian city of Timisoara and the ringleader was later jailed for four years.
Other sextortion rings have been uncovered operating on an “industrial scale” from call centre-style offices in the Philippines.
Investigators believe the problem is rising globally, with South Wales Police alone receiving five reports a fortnight so far in 2018