RPM-MKTG, which has run the championship since its 1998 debut as World Series by Nissan, cited the "continuous and alarming drop in entries" as the main reason for the series' closure.
FV8 has declined since Renault pulled its backing at the end of 2015.
The 2017 finale in Bahrain has attracted only 10 competitors, despite being on the World Endurance Championship support package.
An agreement had been made in the summer to continue supporting the WEC, but the sportscar series' 'super season' announcement had caused some uncertainty over what FV8 would do about its own calendar for 2018.
A series statement said: "Neither World Series Formula V8 3.5 nor any other top single-seater series in the world have reached the ideal number of participating drivers in 2017.
"The continuous and alarming drop in the number of driver entries in the main European single-seater series has forced Formula V8 3.5 to withdraw from the 2018 season racing calendar."
The statement added that a potential FV8 relaunch would be considered if there was enough interest from teams, drivers and sponsors in the near future.
Headed by Jaime Alguersuari Sr, the series was the proving ground for 25 drivers who went on to race in Formula 1, including world champions Fernando Alonso and Sebastian Vettel.
Grand prix winners Heikki Kovalainen and Robert Kubica were also among the series' champions, as were current F1 racers Kevin Magnussen and Carlos Sainz Jr.
Red Bull F1 driver Daniel Ricciardo was a title contender when the championship was known as Formula Renault 3.5 but narrowly missed out to Mikhail Aleshin in 2010 and then had his '11 campaign interrupted by his move to F1.
Pierre Gasly and Brendon Hartley, the latest additions to the F1 grid, are both former FR3.5 racers, as is McLaren's Stoffel Vandoorne.
The series - then branded 'Open Fortuna by Nissan' and using two-litre Nissan-powered Coloni chassis - had immediately launched a driver into F1 in its first season, when 1998 champion Marc Gene earned a Minardi seat for the following year. He was succeeded as champion by then unknown car racing novice Alonso (pictured below).
At its peak, the championship attracted large crowds via ticket promotions and featured Renault F1 demonstrations at its events, with series champions guaranteed F1 tests.
Renault's departure at the end of 2015 immediately led to grids falling despite RPM's best efforts to keep the series viable.
DAMS and Carlin were among the top teams to depart, with Arden following at the end of last year.
This season's WEC tie-up resulted in international expansion and LMP1 prize tests, but grids continued to decline.
Of the six teams still participating, Fortec and the Charouz squad that runs the Lotus operation have both secured places on the Formula 2 grid for 2018.
Lotus driver Pietro Fittipaldi, grandson of double F1 champion Emerson, carries a 10-point lead over Matevos Isaakyan into what has become the final FV8 title decider this weekend.
The 2015 Formula Renault 3.5 season will be notable for being the last with the French company's backing but also produced a worthy champion in Oliver Rowland. PETER MILLS evaluates this year's crop of drivers
Last year's field was extraordinary and hard to match, but the Formula Renault 3.5 grid will still have plenty of talent this season. Glenn Freeman runs through the field ahead of this weekend's season opener
Landing the Fortec seat that took rising star Robin Frijns to the 2012 FR3.5 title was already a good sign for Stoffel Vandoorne. Then McLaren took him under its wing. Peter Mills tells Vandoorne's story so far