The incident was reported at around 8.15 am when the woman Bhawna was crossing the road near Sai Baba temple in Najafgarh, a senior police official said.
She was rushed to a nearby hospital where she was admitted with a fracture in her leg.
The driver -- Sukhbir -- was caught hold by the locals who called up the police.
"A case under Section 279 (rash driving) of the IPC has been registered and the driver of the cluster bus has been arrested," the senior official said.