Many of the victims were asphyxiated by the smoke from the blaze which the fire broke out at around 3:00 pm (2000 GMT) on Friday.
Local media reported that 176 children, aged from six months to five years old, had been in the daycare centre.
Radio reports said there were a number of babies in part of the centre where the fire caused the roof to collapse.
Rachel Levin, Al Jazeera's correspondent in Mexico City, said: "Parents have been lining up outside government buildings, trying to find out information about their missing children.
"Some of the children have been taken to about five local hospitals."
At least 30 children with serious burns were transferred to a specialised hospital across the border in Arizona, according to Mexico's El Imparcial daily.
The origin of the blaze was unclear.
Local media suggested it had started in a neighbouring tyre shop, but the shop's owners denied the reports.
They said they heard an explosion in a warehouse adjoining the centre, suggesting that may have caused the fire.
The local prosecutor's office cautioned against premature conclusions, saying that "it would be adventurous to pass judgement on what caused the fire".
State investigators were attending the scene.
Felipe Calderon, the Mexican president, expressed his "profound pain" to the tragedy, a statement from his office said.
Calderon called on the national social security director, Daniel Karam Toumeh, to personally visit families and injured children in Hermosillo.
The federal government sent three air ambulances and more than a dozen specialised doctors to the scene, the presidential statement said.