Suga, whose real name is Min Yoon-gi, is the third member of the band to enlist after Jin and J-Hope, who began serving in December and April respectively.
The 30-year-old rapper might not be an active-duty soldier due to a torn shoulder labrum for which he underwent surgery in 2020.
He will instead work as a social services officer at an undisclosed location.
BigHit Music, the label that represents both BTS and Suga, has urged fans not to visit his workplace.
The artist said goodbye to BTS fans, known as ARMY, with a message on the Weverse community platform.
"I was able to come this far thanks to you," Suga wrote.
"And the time has come.Â
"I will faithfully complete my duty and come back."
South Korean news agency Yonhap reported Suga told fans to "stay healthy" and that he would see them in 2025.
RM, Jimin, V and Jungkook have yet to begin military service, which lasts at least 18 months.
On Thursday, Hybe, the parent company of BigHit Music, announced it would renew the contracts of the seven members of the band for the second time.
The contracts will become effective in 2025 when the band is scheduled to return to the stage.
BTS announced a hiatus in October last year to focus on personal projects and perform military service.
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