Images have emerged purportedly showing Wagner fighters training Belarusian soldiers at a base south-east of Minsk
The DPSU says it is assessing how many "militants" are in Belarus, which also shares a border with Ukraine, as well as their exact location and goals.
One unconfirmed report said a convoy of some 60 Wagner vehicles rolled over the border into Belarus early on Saturday.
In June, Wagner's mutiny challenged President Vladimir Putin's authority.
A deal ended the 24-hour rebellion, which saw the troops seize a city and march on Moscow - aborting it just 200km (124 miles) from the capital.
Under the agreement, Wagner fighters were told they could join either the regular Russian army or go to Belarus, a close ally of Russia. The Wagner leader, Yevgeny Prigozhin, was also offered a move to Belarus, however his current whereabouts are unknown.
Wagner is a Russian private military company made up of mercenary fighters - many of whom were recruited from Russian prisons. They have fought some of the bloodiest battles since Russia launched its full-scale invasion of Ukraine in February last year.