"If you have seen this little girl please go to the local authorities or the police with any genuine information.
"Please, please help us."
The three-year-old was snatched from her family's holiday apartment in Praia da Luz, Portugal, on the evening of Thursday, May 3.
Beckham, set to leave Real Madrid for a career in America, is the latest figure from the football world to appeal for help.
Manuel Fernandes, an Everton midfielder and Portuguese international, said: "I was very distressed to hear that Madeleine was taken from the Portuguese Algarve.
"This is a very worrying time for all her family and I appealto anyone with any information at all to come forward.
"Please help the McCann family find their daughter."
Club captain Phil Neville, in a statement posted on the club's website, said: "Everton has fans all over the world and I know that they, along with everyone connected with the football club, are hoping and praying for Madeleine's safe return.
"Our thoughts are very much with the family at this extremely distressing time."
As well as Everton, other clubs have taken Madeleine's disappearance to heart.
Celtic - based in Glasgow, where her father Gerry is from - and Aberdeen players wore yellow ribbons during their match on Saturday.
Earlier, Manchester United and Portugal star Cristiano Ronaldo appealed for people with information to come forward, adding: "I was very upset to hear of the abduction."
Chelsea captain John Terry, flanked by Portuguese team-mate Paulo Ferreira, said: "We were devastated to hear that young Maddie was abducted.
"It's a terrifying thing for her family to go through. She's only young so please, please, please come forward."
