A separate blast in the town of Tatvan wounded five soldiers when their vehicle passed over an explosive left in a ditch by the road, security sources said.
The most intense fighting since the 1990s has engulfed Turkey's mainly Kurdish southeastern region since July when Ankara launched air strikes against the armed Kurdistan Workers Party (PKK) in Turkey and Iraq. More than 100 security personnel and hundreds of militants have been killed.
The children were hurt in Diyarbakir's historic district of Sur, scene of recent street clashes between security forces and the PKK. A hospital official said the blast was caused by a bomb but did not elaborate.
Diyarbakir is the largest city in southeastern Turkey, home to most of the country's 15 million Kurds, Reuters reported.
Authorities have sporadically imposed a curfew in Sur, a narrow warren of streets where vehicles cannot pass. It is also home to historic churches and mosques and a Roman-era fortress.