Two of the women, one in a wheelchair, had to be cut free.
They were hit by a large limb from a lombardy poplar tree on Southwick Recreation Ground that broke off in high winds just before 10am.
One of the women was able to crawl out when the tree struck, but she hit her head and hurt her back when some of the trees falling branches struck her as it fell.
The second woman, a regular user of the nearby Sussex MS Treatment Centre, was brought out with the help of firemen. The tree struck her hip and injured her legs.
The third woman was freed after around three-quarters of an hour, during which she was slipping in and out of consciousness.
All three were taken to hospital by ambulance. Although the air ambulance was called to the scene, the paramedics made the decision to use a conventional, road-going, ambulance to make the trip to hospital.
The tree and the immediate vicinity has now been cordoned off and the area is being made safe.
John Mitchell, director for communities at Adur and Worthing councils said: “This must have been a terrifying incident for all concerned and the councils are doing everything in their power to ensure that our parks are safe for all to enjoy.
“Adur District Council is responsible for the recreation ground and takes the safety of all visitors extremely seriously. Our investigation will be immediate and thorough, and we will make the results public as soon as we have them.
“Our thoughts are with the ladies involved. We all wish them a speedy recovery and wish to thank our 999 response teams for their swift and decisive actions.”
Read more in the Shoreham Herald on Thursday.