Prosecutor Miroslav Markovic told reporters that the explosion at the Kovaci cemetery in Sarajevo's Old Town took place at 03.04 hours Friday.
According to available information, Izetbegovic's remains have not been damaged.
Prosecutor Markovic said it was being assumed that the motive behind the attack was of a political nature, but that further investigation needed to confirm the speculation.
The head of the Agency for Investigations and Protection (SIPA), Sredoje Novic, whose arrival at the scene attached additional importance to the attack Izetbegovic's grave, said this act of terrorism was inhumane.
The Interior Ministry of the Federation of Bosnia-Herzegovina, Mevludin Halilovic said additional security measures would be introduced across the country.
The Chairman of the Bosnian collective Presidency, Sulejman Tihic, said in a statement this was an act of terrorism and crime and an attempt to destabilise the situation in the country.
The international community's High Representative for Bosnia-Herzegovina, Christian Schwartz Schilling also visited the crime scene and harshly condemned the the attack. His office issued a statement expressing an outrage and sadness. Stressing that Izetbegovic was an exceptional person in difficult times, the High Representative said that Izetbegovic's memory still lived in the hearts of many.
Bosnian State Minister for Human Rights Mirsad Kebo said light would be shed on the case in the next three days. Bosnian Federation Prime Minister Ahmet Hadzipasic and the president of the Party for Bosnia-Herzegovina, Haris Silajdzic also condemned the attack on Izetbegovic's grave.