His assessment comes as outgunned and outmanned Ukrainian forces struggle to hold back Russian troops, who have gained ground in recent months and are expected to soon step up their offensive.
"In our opinion, a rather difficult situation awaits us in the near future," Kyrylo Budanov told the BBC's Ukrainian service.
"But it is not catastrophic and we need to understand that. Armageddon will not happen, as many people are now saying," he said.
"But there will be problems starting from mid-May. I am talking about the front in particular... It will be a difficult period in mid-May, early June," Budanov said.
Russia has in recent weeks regularly claimed new gains in eastern Ukraine.
On Monday, Russia's defence ministry said its troops had seized the village of Novomykhailivka, some 20 kilometres (12 miles) away from Vugledar, which Russian forces have been trying to capture.
It announced other gains near the eastern town of Chasiv Yar over the weekend.
Taking control of Chasiv Yar's strategic heights would open the road for Russia to other important towns in the Donbas region of eastern Ukraine.
Ukrainian President Volodymyr Zelensky has said Russian forces want to capture Chasiv Yar by May 9, when the Kremlin marks the Soviet Union's victory over Nazi Germany in World War II.
Kyiv has for months struggled with a growing ammunition shortage but that is expected to improve in the coming weeks, with the United States on Saturday finally approving a $61-billion package of military aid to help battle Moscow.
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