President Volodymyr Zelenskiy dismissed the heads of regional recruitment centres in August after widespread allegations of criminal abuse and corruption.
The SBI said 21 indictments against 35 individuals had been sent to court, and that another 58 people had been identified as suspects.
It also said it had documented around $110,000 worth of alleged bribes and that courts had seized around $88,000 worth of property.
"Although the vast majority of...employees conscientiously perform their duties, in many regions there are cases of abusing official positions or exceeding authority," it said in a statement.
Kyiv is aiming to improve military recruitment as it presses on with a more than four-month-old counteroffensive to drive Russian forces out of territory in the east and south of Ukraine following Moscow's full-scale invasion last year.
Zelenskiy and his government are also keen to show that Ukraine is fighting corruption after setting their sights on membership of the European Union.
"The Bureau warns officials who intend to use their official position for their own profit during wartime: you will definitely be exposed and prosecuted," the SBI said.
(Reporting by Dan Peleschuk)
