John McCann, brother of Madeleine's father, Gerry, said: "We have no comment to make, because we know no more than we have seen on the news."
Madeleine's great uncle, Brian Kennedy, said he did not know any details about the arrest of the man.
Kennedy said: "We are trying not to get our hopes up too much because they so frequently get dashed."
Madeleine disappeared on May 3 after her parents left her and her brother and sister, two-year-old twins, alone in their room.
They had gone to visit a restaurant inside their hotel complex in Praia da Luz, a tiny resort town in Portugal's Algarve region.
Police have identified just one suspect in the case, but had made no arrests before Thursday.
A month ago, Portuguese police said they were searching for a suspect, identified as a white man between 35 and 40-years-old, in connection with the girl's disappearance.
They said the suspect had been wearing a dark jacket and beige trousers on the day the girl disappeared, and was spotted possibly carrying the girl near to where she had vanished.
Police have received countless tip-offs in the last two months, and the girl's parents have launched an international campaign to find her, enlisting the aid of celebrities such as David Beckham and JK Rowling, author of the Harry Potter books.