The Electoral Commission said every visitor to the social networking site on Saturday will be asked if they have already signed up to vote. If not, they will be redirected to the commission's site where they can register.
At least 3.5 million people failed to register for the 2001 election and the commission estimates there may still be millions in the same position.
Young people are among the biggest users of Facebook, but are traditionally the hardest to persuade to cast their vote.
"If you're not registered, you can't vote," said Clinton Proud, head of campaigns at the Electoral Commission.
The number of voters who go to the polls has fallen over the last 100 years. Turnout at the last election in 2005 was 61.4 percent. By contrast, turnout in the early 1950s was above 80 percent.
It is lowest among 18-24-year-olds, falling to 37 percent in 2005 from 39 percent at the 2001 election, according to MORI estimates.
In a report after the 2005 vote, the watchdog blamed the low turnout on the perceived similarities between the main parties and a campaign seen as "at best lackluster and at worst negative in tone and too stage-managed."
Some voters felt their vote would make no difference because "nothing will change" whoever wins, the report added.
Younger people are less likely than older voters to see going to the polls as a civic duty, it said.
Richard Allan, Facebook's director of policy, said the site had 23 million users in Britain, of all ages and backgrounds.
"We are therefore uniquely placed to reach unregistered voters," he said.
Voters must register by April 20 if they want to vote in an election that polls suggest will be the tightest in 20 years.
The main parties have taken a leaf out of President Barack Obama's campaign and embraced email and the web in what some are calling "Britain's first internet election.