Taking place outside an army office in the central town of Pavlograd, Sunday's blast was the latest in a series of similar incidents, just a day after a separate blast killed one person.
Without giving a possible cause, the Dnipropetrovsk regional police said an investigation was ongoing into the blast which happened towards at 6:40 pm (1640 GMT).
"According to preliminary information, a man was wounded by the explosion of a unidentified object," the force said in a statement.
Attacks on recruiting authorities are rare but not unheard of in Ukraine and Russia as tensions run high over efforts to mobilise men for the war.
On Saturday a blast in Rivne, a town in northwest Ukraine, killed one person and wounded six at a centre responsible for drafting men into its army, outmanned by its Russian opponents.
Authorities did not say what caused the explosion or reveal details on the casualties.
Earlier Saturday, a man with a hunting rifle shot dead a Ukrainian army recruitment soldier and escaped with a conscript before both were caught by police, according to authorities.
At the end of October, Ukraine announced it planned to mobilise 160,000 conscripts to bolster its army over the next three months.
Many Ukrainians consider the enlistment system, which has been at the heart of numerous corruption scandals, to be unfair.
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