The goalkeeper, on loan from Wolves, qualifies for the southeast Europe nation through his father Bojan, and has one cap, which he earned in November 2019.
The 23-year-old will join up with the national team for qualifiers against Latvia, Gibraltar and Norway – where he could face Dortmund superstar goal machine Haaland – between March 24 and March 30.
That means he is certain to at least miss Shrewsbury fixtures at Burton on March 23 and at home to Portsmouth on March 27.
The goalkeeper has previously said he is proud of his Montenegrin roots and gaining further international accolades were a target.
Sarkic, who was born in Grimsby but spent his upbringing in London and Brussels, has enjoyed an impressive first full season of senior football in League One with Shrewsbury. He has made 23 appearances in all competitions and kept several crucial clean sheets since Steve Cotterill was appointed in November and Town surged up the table.