Paul Harsley’s side will travel to Montgomery Waters Meadow on Tuesday 3 December for a 7.30pm kick-off.
City’s youngsters reached the last 32 after topping Northern Group F having recorded wins over Rochdale and Bradford City, before a defeat against Bolton Wanderers.
It meant we were guaranteed a home tie in the knockout stage, but we have received special dispensation to play away from home against Shrewsbury.
Sam Ricketts’ side are currently 11th in League One and qualified for the second round of the EFL Trophy thanks to a second placed finish in Northern Group D.
Ticket information will be confirmed in due course.
Full Round Two draw:
Port Vale vs Mansfield
Accrington Stanley vs Bolton Wanderers
Leicester City U21s vs Doncaster
Salford City vs Wolves U21s
Everton U21s vs Fleetwood Town
MANCHESTER CITY vs Shrewsbury Town
Blackpool vs Scunthorpe United
Manchester United U21s vs Tranmere Rovers
Colchester vs Stevenage
Walsall vs Chelsea U21s
Brighton U21s vs Newport
Portsmouth vs Northampton
MK Dons vs Coventry
Exeter vs Oxford United
Peterborough vs Ipswich
Bristol Rovers vs Leyton Orient