Siddaramaiah and four others, including Home Minister G Parameshwara who were also on board, were safe, Assistant Commissioner of Police P Nagesha Kumar told PTI.
The chopper did not suffer any damage in the bird hit, he said.
He said the Chief Minister and others left for Shravanabelogala in Hassan district as scheduled by the same helicopter a few minutes later after clearance, adding, they landed at the destination.
Mr Siddaramaiah was on an official visit to Shravanabelogala to launch developmental schemes for "Mahamasthakabhisheka", a once in a 12-year event at the Jain pilgrimage centre scheduled for February next year.
Mahamasthakabhisheka is the anointment of the 57-foot high monolithic statue of Jain deity Lord Gommateshwara, also known as Bahubali, located on Vindyagiri at Shravanabelogala.