The attacks have been blamed on locals who have voiced criticism of the McCanns' new campaign for information on their daughter's whereabouts.
The fresh appeal is focused on the area where Madeleine, three, went missing on May 3 2007 during a family holiday.
Around 10,000 leaflets are being handed out and posted through letterboxes in Praia da Luz and the nearby towns of Lagos and Burgau.
The Algarve campaign is being backed by billboards, posters and advertising on local buses.
The appeal has been criticised by part of the local population who have dismissed it as a waste of time and claim it is affecting the resort's image.
Resident Maria Afonso said: "It's stupid to think this campaign will bring Madeleine back two years after she disappeared.
"It's just sullying the reputation of the Algarve." Local Rute Fernandes added: "It's a waste of time. "There's not a single person on the Algarve that is unaware of this case and doesn't know who Madeleine McCann was." Family spokesman Clarence Mitchell has said the appeal's aim is to collect the vital clue that could lead to Madeleine being found.
The official Find Madeleine Fund said in a statement earlier this week: "At the time of Madeleine's disappearance the emphasis was placed more on international appeals, and it has been recognised that the local Portuguese residents of Praia da Luz and the surrounding areas have never been properly asked about information they may have to give.
"The purpose of the current campaign is to do that - ask the local Portuguese residents for information to help to find Madeleine."