The women were from the Brotton area of Cleveland and aged 67 and 63. The older woman was critical but stable in hospital. The other woman had less serious injuries.
In East Yorkshire, another tree fall left a driver in hospital. The motorist was injured when the tree hit a Ford Focus car on the A165 Beverley to Driffield road, close to Leconfield.
Humberside firefighters were called to a series of weather related incidents including fallen chimney stacks and collapsing scaffolding, but spokesman Glenn Ramsden said some of the call-outs were to structural problems which could have been caused by the earthquake on Wednesday morning.