Midfielder Evans has been included in Wales Under 21s' squad for their UEFA U21 Championship Group 5 Qualifier against Denmark at the Aalborg Stadion on Friday 9 October 2015.
During his loan spell with City, Evans has already played in Wales' previous UEFA U21 qualifier in Luxembourg.
Defender Burke has been named in England Under 20s' travelling party to the Mercedes-Benz Elite Cup in Germany.
The Three Lions are scheduled to play against the Netherlands (Wednesday 7 October 2015), Turkey (Saturday 10 October) and hosts Germany (Tuesday 13 October) over the course of seven days.
While playing with the Bantams, Burke made his international debut at Under 20 level for England in their friendly contest with Czech Republic earlier this month.
As result of Evans and Burke's call-ups, the pair are now expected to miss City's Johnstone's Paint Trophy tie with Barnsley (Tuesday 6 October 2015) and the Sky Bet League 1 fixture against Blackpool (Saturday 10 October).