The 39-year-old was rescued and taken to hospital after viewing the house in Malmesbury, Wiltshire, on Saturday.
Estate agent Strakers said the well was "hidden" within shrubbery and "not clearly visible or identifiable" when it had assessed the garden.
The house had been offered for sale following the owner's death.
Antony Bulley, Strakers managing director, said: "We were clearly shocked when this incident occurred.
"Our immediate concern on learning of the incident was for the wellbeing of the lady concerned, and we are grateful for the prompt actions of the emergency services in dealing with this awful incident.
"We are cooperating with authorities and will also carry out our own investigation into what happened, and will look to see what procedures can be put in place to identify hidden and unannounced hazards and to ensure this cannot happen again."
The rescue was heard by Kitty Wiles, a neighbour of the house in The Triangle, who said the woman's "predicament was really dreadful".
"Thank goodness the people in control were very calm and very capable, working together as a team and seeming to know exactly what to do," she added.
An estate agent for a home where a prospective buyer fell 30ft (9m) into a garden well has said it was "shocked" by the incident.