The girl was walking with her family in the Donnington Wood area on Saturday when the incident happened.
Police said two cyclists rode past at speed and knocked her to the ground.
Officers said one of the cyclists was white and the other was black, with both aged between 13 and 15-years-old.
A spokesman for the force said: "We are appealing for witnesses following an incident which left a two-year-old with facial injuries in Donnington Wood, in Telford.
"Police were called, with reports that at around 12.30pm on Saturday, June 27, when a family was walking their dog through the pathway between Asda and McDonald's, two cyclists rode through at high speeds, knocking the young girl to the ground.
"The girl was taken to hospital with serious facial injuries requiring surgery.
"The first cyclist to pass them is described as a black male between 13 and 15-years-old, the second was a white male around the same age, with blonde hair and was wearing grey jogging bottoms with a grey T-shirt."
Anyone with information is urged to contact police on 101 quoting incident 234s 280620.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org