The Sheffield United centre-forward is one of four Yorkshire-based players in Steve Clarke's latest squad, along with team-mate John Fleck, Leeds United's fit-again captain Liam Cooper and Sheffield Wednesday full-back Liam Palmer.
Scotland are away to Cyprus and Kazakhstan.
McBurnie has been a substitute in the last two matches, coming on in the 85th and 75th minute. He was charged with drink driving after an incident in Leeds city centre during the last international break.
In his place Lys Mousset and, despite his ongoing search for a first goal of the season, David McGoldrick have been in excellent form for the Blades.
Fleck has started nine of Sheffield United's 11 matches this season, and has been crucial to a start which has put them sixth in the table.
Cooper made his first start after a groin injury in Leeds's 2-0 win over Queens Park Rangers at the weekend. His Leeds club-mate Tyler Roberts is in the Wales squad to play Azerbaijan and Hungary.
Palmer, who made his international debut in March's reverse fixture against Kazakhstan, has been part of the second-best defence in the Championship. Only Leeds have conceded fewer than Sheffield Wednesday's 12 goals.
Mo Besic, on loan at Bramall Lane from Everton, has been named in Bosnia and Herzegovina's squad for qualifiers against Italy and Liechtenstein.
The Premier League and Championship go on a two-week break after this weekend's round of fixtures while the international games take place.