The website, which is being promoted by The Sun Online, features a downloadable sweepstake chart for fans to organise their own draws. Help the Hospices asks site visitors to give half of the money raised through the sweepstake to the winner and donate half to the charity.
"People will be doing sweepstakes in their offices anyway, and we thought this was a good opportunity to make the most of the nationwide enthusiasm for the competition," said Stephen Ballantyne, corporate fundraiser at Help the Hospices.
"We're hoping the initiative will raise about £10,000 in total for hospice care, but it's possible that we could smash through that target."
The charity also hopes to capitalise on those who are not so enthusiastic about four weeks of non-stop football. Among the fundraising ideas on the site is running a 'swear box' "for colleagues who won't stop talking about the games".
This is one of several suggestions on the fundraising ideas page on the sweepstake site.
The Sun is promoting the sweepstake with a link from its website. The newspaper has been involved with the charity since January, when it launched a campaign to increase children's hospice funding with the Association of Children's Hospices.
England manager Sven-Goran Eriksson has lent his support by leaving a message on the site encouraging fans to take part. It reads: "The hospice sweepstake is a fantastic way to get into the spirit of this year's World Cup. You'll be raising funds to help hospices continue to provide time and care for people with a terminal illness."
The Football Association has also given permission for its official tournament wallchart to be downloaded from the site.
The site has registered more than 5,500 unique hits since it went online last week and nearly 17,000 tournament wallcharts have been downloaded. Ballantyne said the site would remain online for up to three months after the tournament has finished to allow people time to send in the money they have raised.
The sweepstake website follows the success of Help the Hospices' World Cup wristbands, which have been on sale in Argos stores since May and have raised more than £65,000 for the charity.