Witnesses said they saw two youths hanging off the tail fin and swinging on the pilot's door of the Kent Air Ambulance helicopter after it landed in a field near Vine Cricket Ground in Sevenoaks at around 4.30pm on Sunday.
When challenged, they became aggressive and one grabbed the pilot around the throat, Kent Police said.
The attack meant that the baby had to be taken to hospital by road. The aircraft was then grounded for a day so it could be inspected by an engineer to check for any damage.
Kent Air Ambulance chief executive John Tickner said: "I find it incredulous that anybody would want to attack a charity air ambulance and its crew, whose sole purpose is to help seriously injured people in their time of need."
A 19-year-old and a teenager, 17, have been arrested over the incident and have both since been released on bail while inquiries continue.