Reporters saw the body of the child killed as rocket fire hit a residential area in Artemivsk. It was not immediately clear who was responsible for the attack.
The shelling occurred as Russian-backed separatists mount a major effort to capture Debaltseve, a strategic railway hub south of Artemivsk, ahead of the ceasefire, which begins a minute after midnight tonight.
The leaders of Russia, Ukraine, Germany and France signed a peace deal on Thursday after marathon talks in the Belarusian capital of Minsk.
Earlier, Vladislav Seleznyov, spokesman for the Ukrainian army general staff, said eight soldiers were killed and 34 wounded over the previous day.
Regional authorities loyal to Kiev reported four civilian deaths in areas under their control, while rebels said seven people were killed in artillery attacks on the separatist-held cities of Luhansk and Horlivka.
Separatist forces have nearly encircled a Ukrainian garrison in Debaltseve, where all but a few thousand civilians have fled to areas away from the front.
Only one major road had remained linking the town to government-held territory, but Ukrainian access to that supply route looked to have been compromised with the apparent capture of the village of Lohvynove, which lies along the road, just north of Debaltseve.
The Donbass Battalion, a unit with Ukraine’s National Guard engaged in battles around Lohvynove, said in a statement that captured combatants had confirmed Russian troops were actively involved in battles.
Moscow denies providing manpower and weapons to the rebel forces, although the sheer quantity of powerful weapons at the separatists’ disposal has increasingly strained that position.
Elsewhere, by the Azov Sea in the south east, Ukrainian government troops say they clawed back a handful of villages. Troops there have denied reporters access to the areas at the centre of those operations.
The ceasefire is to be monitored by the Organisation for Security and Cooperation in Europe’s observer mission in Ukraine.
OSCE secretary general Lamberto Zannier said in Kiev that he hoped hostilities would be halted by the deadline.
“We would really hope to see a decrease already between now and that moment,” he said.
Mr Zannier said combatants would have to do more to enable the OSCE peace-monitoring mission, which uses drone cameras, to properly fulfil its mandate.
“Aerial vehicles have been targeted more than once, monitors have been taken hostage, so we need a change of attitude,” he said.
The next step, to begin on Monday, is to form a sizeable buffer zone between Ukrainian forces and Russia-backed rebels.
Each side is to pull heavy weaponry back from the front line, creating a zone roughly 30-85 miles wide, depending on the calibre of the weapons.
The withdrawals are scheduled to be completed within two weeks.
Other thorny political questions, including a degree of autonomy for the disputed eastern regions, are to be settled by the end of the year.
The peace deal envisions an amnesty for people involved in the conflict, but the vague terms of that provision will be the subject of further negotiation.