There is contention about this issue among Muslims, but many maintain that prayer at the tombs of saints and revered figures is idolatrous in itself, and therefore must be suppressed -- by violence if necessary. A hadith puts it in the mouth of Muhammad: "Narrated 'Aisha and 'Abdullah bin 'Abbas: When the last moment of the life of Allah's Apostle came he started putting his 'Khamisa' on his face and when he felt hot and short of breath he took it off his face and said, 'May Allah curse the Jews and Christians for they built the places of worship at the graves of their Prophets.' The Prophet was warning (Muslims) of what those had done." -- Bukhari 1.8.427
Also, "Islamists believe Sufi shrines are sacrilegious."
"Rebels burn Timbuktu tomb listed as U.N. World Heritage site," from CNN, May 5:
Bamako, Mali (CNN) -- Elderly men were keeping watch Saturday over Timbuktu's main library after Islamists burned a tomb listed as a UNESCO World Heritage site.
The attacks Friday were blamed on Ansar Dine, a militant group that seeks to impose strict Sharia law.
The ancient city in Mali was captured by at least two separatist Tuareg rebel groups -- one of which is Ansar Dine -- in an anti-government uprising in the northern part of the country that began in January.
The rebels burned the tomb of a Sufi saint where people come to pray, said Sankoum Sissoko, a tour guide familiar with the place. He said the library and other heritage sites remained under threat.
Baba Haidara, a member of the National Assembly, called for UNESCO and the greater international community's help restoring the shrine and freeing the city.
"They attacked the grave, broke the doors and windows and ripped and burned pieces of white clothing that surrounded the tomb of the saint in front of everyone," said Haidara, who is from the central Mali city. "With their attack, the militants touched the heart of Timbuktu. They picked Friday because they know many people visit the shrines on this day."
Sufism is a mystical dimension of Islam, and Islamists believe Sufi shrines are sacrilegious. As such, they have mounted attacks against Sufi sites in several nations.
Sissoko said the attackers were dressed in signature Ansar Dine black robes and turbans. Timbuktu residents, he said, were ready to take up arms against the rebels, who have been linked to al Qaeda.
Religious leader Baba Cheick Sekou said the occupying rebel groups have no respect for Timbuktu's religious and historic importance.
Sekou said he feared for the protection of the prestigious Koranic Sankore University and ancient manuscripts that are kept there, as well as other tombs and mosques of historic significance.
"All Muslims know the tomb is a holy place," he said. "It's not something you attack and destroy. It's anti-Islamic. People in the community are angry."
Actually the ancient manuscripts are probably safe unless the jihadis deem them useful. Sekou's worries are out of focus because he appears unaware (or unwilling to credit) the prohibition on prayer at graves as an explanation for Ansar Dine's actions.