Fire Brigade sources confirmed that 17 students were killed in the incident at the Takshashila Arcade building in Sarthana area.
The fire engulfed the third and fourth floor of the Taxshila Complex here, the official said.
Students, mostly teenagers, died "either due to suffocation or jumping off from the complex", he said.
"Around 10 students on fourth and third floor jumped off to the ground to save themselves from fire and smoke", said a fire official.
Visuals on TV channels showed students jumping off the third and fourth floors of the building.
Locals helped in the rescue operation to save the stranded students and other occupants of the building.
Prime Minister Narendra Modi expressed grief over the tragic incident. He tweeted, "Extremely anguished by the fire tragedy in Surat".
Gujarat CM Vijay Rupani has ordered an investigation in the matter and has ordered to give Rs 4 ex-gratia to the families of the deceased.
Initial reports suggest that numerous children trapped in fire panicked and jumped as fire engines battled the blaze.
Five more students who were injured were taken to nearby hospitals, he added. "I pray for the families who have lost loved ones, & for the speedy recovery of those injured". "Have asked the Gujarat Government and local authorities to provide all possible assistance to those affected", he tweeted.
The cause of the fire is not yet clear, but officials said the blaze spread through packed classrooms because of the material used in the roof.