Ukraine has a long history of corruption and shaky governance, though there have been few examples since last year's invasion as Kyiv has fought back Russian forces and received Western financial and military support.
On Sunday, anti-corruption police said they had detained the deputy infrastructure minister on suspicion of receiving a $400,000 kickback to facilitate the import of generators into wartime Ukraine last September.
Separately, a newspaper investigation accused the Defence Ministry of overpaying suppliers for soldiers' food. The minister said the allegations were untrue, and that the supplier had made a technical mistake and no money had changed hands.
The National Anti-Corruption Bureau said it was aware of the media report and that it was investigating the possible crime of appropriation of funds or abuse of power with regard to procurement worth over 13 billion hryvnia ($352 million).
David Arakhamia, head of Zelenskiy's Servant of the People party, said it had been made clear since Russia's invasion that officials should "focus on the war, help victims, cut bureaucracy and stop dubious business".
"Many of them got the message. But many of them did not unfortunately. We're definitely going to be jailing actively this spring. If the humane approach doesn't work, we'll do it in line with martial law," he said.
Before last year's invasion, fighting corruption was the principal theme for Zelenskiy, a political novice swept into power in 2019 on a promise to clean up crooked institutions. In his nightly video address on Sunday, Zelenskiy said measures would be announced this week.
"I want this to be clear: there will be no return to what used to be in the past, to the way various people close to state institutions or those who spent their entire lives chasing a chair used to live," Zelenskiy said.
Timofiy Mylovanov, a former minister for the economy, trade and agriculture, praised the government's "proactive and very fast" response to the corruption allegations. He said the deputy minister had been immediately fired and pointed to society's "unprecedented" level of attention in the matter.
A committee in parliament reviewed the situation around the Defence Ministry procurement on Monday and listened to officials give accounts of what had happened.
Several Ukrainian media outlets have reported that a number of cabinet ministers and senior officials could be sacked imminently as Zelenskiy tries to make the government more effective and streamlined.
Ukraine, whose economy shrank by a third last year, is hugely dependent on Western financial aid and donors such as the International Monetary Fund and EU have repeatedly asked for more transparency and better governance.
($1 = 36.9250 hryvnias)
(Editing by Peter Graff and Timothy Heritage)
By Tom Balmforth and Olena Harmash