Oleksii Reznikov said Moscow had amassed thousands of troops and could "try something" to mark the anniversary of the initial invasion last year.
The attack would also mark Russia's Defender of the Fatherland Day on 23 February, which celebrates the army.
Meanwhile, three people have died in an attack on the city of Kramatorsk.
Eight others were wounded in the city in Donetsk region after a Russian missile struck a residential building, the provincial governor said.
The toll is expected to rise as rescuers comb through the wreckage.
"The only way to stop Russian terrorism is to defeat it," Mr Zelensky wrote on social media about the attack. "By tanks. Fighter jets. Long-range missiles."
Ukraine has recently renewed calls for fighter jets to help protect itself from air attacks after Germany, the US and the UK agreed to send them tanks.
Mr Reznikov said Moscow had mobilised some 500,000 troops for the potential offensive.
In September, Russian President Vladimir Putin announced a general mobilisation of some 300,000 conscripted troops, which he said was necessary to ensure the country's "territorial integrity".
But Mr Reznikov suggested that the true figure recruited and deployed to Ukraine could be far higher.
"Officially they announced 300,000 but when we see the troops at the borders, according to our assessments it is much more," he told the French BFM network. The BBC cannot independently verify this figure.
Russia has claimed recent gains in the eastern Donbas region and its forces say they are moving in on the front-line town of Bakhmut after a battle that has lasted months and led to heavy loss of life on both sides.
Last month, Russian mercenaries and regular soldiers seized the nearby town of Soledar and on Wednesday a Russian-appointed official, Yan Gagin, said Bakhmut was "operationally surrounded".
The US-based Institute for the Study of War (ISW) recently said that Moscow could seek to "undertake a decisive action" and launch a "big offensive" in the east.
Mr Reznikov said Ukraine's commanders would seek to "stabilise the front and prepare for a counter-offensive" ahead of the rumoured Russian advance.
"I have faith that the year 2023 can be the year of military victory," he said, adding that Ukraine's forces "cannot lose the initiative" they have achieved in recent months.
The defence minister was in France to strike a deal to purchase additional MG-200 air defence radars, which he said would "significantly increase the capacity of the armed forces to detect air targets, including winged and ballistic missiles, and drones of various types".
Mr Reznikov's comments come as Ukrainian intelligence alleges that President Putin has ordered his forces to seize the Donbas before the end of spring.
But speaking on Monday, Nato Secretary-General Jens Stoltenberg warned that there were no indications that Mr Putin had limited his military goals to seizing eastern regions of Ukraine.
"That they are actively acquiring new weapons, more ammunition, ramping up their own production, but also acquiring more weapons from other authoritarian states like Iran and North Korea," Mr Stoltenberg said.
"And most of all, we have seen no sign that President Putin has changed his overall goal of this invasion - that is to control a neighbour, to control Ukraine. So as long as this is the case, we need to be prepared for the long haul."
BBC
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