Police said that a grey Ford Focus had crashed with a lorry on the A41 between Tern Hill and Newport, near to Lavender Cottage in Sutton Heath.
The woman was 35 and the baby was 11 months old. Both died at the scene.
West Mercia Police officers, who are appealing for information about the crash, said that it took place at around 1am today.
A spokesman for the police said: "Officers are appealing for information after a collision in north Shropshire where a woman and child very sadly died.
"It happened around 1am this morning on the A41 between Newport and Tern Hill near Lavender Cottage.
"A grey Ford Focus travelling from Newport collided with [another vehicle].
"Tragically, a 35-year-old woman and an 11-month-old child died at the scene."
Several ambulance crews and paramedic officers attended the scene. The driver of the HGV was assessed by ambulance responders but did not require hospital treatment.
A West Midlands Ambulance Service spokeswoman said: “The two occupants of the car, a woman and a young child, were in a critical condition. Crews worked quickly as a team to provide advanced trauma care with assistance from police and fire colleagues.
“Tragically, despite the best efforts of everyone, nothing could be done to save the woman and child and they were both confirmed deceased on scene."
The police spokesman continued: "Officers are asking anyone who witnessed the incident, saw the grey Ford Focus being driven in the area, or captured the car or the incident on dash cam to please get in touch."
Anyone with any information is asked to visit westmercia.police.uk/tua/tell-us-about/ quoting incident 14 of February 15.
It comes days after a crash on the A518 near Newport in which a woman died at the scene. A 19-month-old toddler, who was a passenger in the car, succumbed to her injuries on Monday.
A crash also occurred on the M54 early this morning, with eastbound drivers delayed near Albrighton.