Acting president Oleksandr Turchynov told the parliament in Kiev that rebels used a portable air defence missile to bring down the helicopter. He said 14 people died, including General Serhiy Kulchytskiy.
One soldier was badly wounded, but information from the scene is still being clarified.
Slovyansk, a city of 120,000 residents 100 miles from the Russian border, has become the epicentre of fighting between pro-Russia insurgents and government forces in recent weeks.
Its residential areas have regularly come under mortar shelling from government forces, causing civilian casualties.
A helicopter went down amid a trail of black smoke. Gunshots were heard in Slovyansk near the crash site and a Ukrainian air force jet was seen circling above.
Mr Turchynov said the helicopter was flying troops to a hill outside Slovyansk where Ukrainian forces have set up positions.
Gen Kulchytskiy had served in the Soviet army and was in charge of combat training for Ukraine’s National Guards.
Slovyansk is in the Donetsk region, one of the two provinces in eastern Ukraine that have declared independence from the government in Kiev.
The Kiev government condemns the insurgency embroiling the east as the work of “terrorists” determined to destroy the country and accuses Russia of fomenting it.
Russia denies the accusation, saying it has no influence over rebels, who insist they are simply protecting the interests of Russian-speakers in the east.
Nevertheless, fighters from Russia, including from the battle-hardened region of Chechnya, have been appearing recently in separatist ranks.
It was reported that 33 Russian citizens were among the rebels killed in the city in fighting earlier this week.
Dozens of men were killed – some insurgent leaders said the death toll might be as many as 100 fighters – when Ukrainian forces used combat jets and helicopter gunships on Monday to dislodge the rebels who tried to take control of the city airport.
Also yesterday, an insurgent leader confirmed that his fighters were holding four missing observers from the Organisation for Security and Co-operation in Europe (OSCE) but promised they would be released shortly.
Vyacheslav Ponomarev, self-proclaimed “people’s mayor” of Slovyansk, said the monitors – who are from Turkey, Switzerland, Estonia and Denmark – were safe.
“I addressed the OSCE mission to warn them that their people should not over the coming week travel in areas under our control. And they decided to show up anyway,” Mr Ponomarev said.
“We will deal with this and then release them.”
The OSCE had lost contact with the team in Donetsk on Monday evening. Their teams have been deployed to Ukraine to monitor the security situation following Russia’s annexation of Crimea and the rise of the pro-Russia separatist insurgency in eastern Ukraine. They also observed Sunday’s presidential vote, won by billionaire sweet magnate Petro Poroshenko.
Mr Poroshenko has promised to negotiate with people in the east, but also vowed to uproot the armed rebels.