Four team members were initially sent to hospital for treatment after the fire but three have been released.
The remaining team member in hospital will be flown back to the UK by Wednesday to continue his treatment.
A statement said he was in "good spirits" and in communication with his family.
Four Caterham team members and one from Force India were also treated in the circuit medical centre, but later released.
The incident happened as the Williams team - including Sir Frank Williams, a wheelchair user - were in the garage celebrating their driver Pastor Maldonado's victory in the race.
The statement said the team was looking into the cause of the fire in collaboration with the FIA and the local authorities in Spain.
Team principal Williams said on Monday: "I was pleased to welcome back to the factory the majority of our team this morning.
"One of our people remains in Spain for further medical assistance but we are all looking forward to his imminent return.
"Everyone at Williams F1 is extremely relieved that this event was contained as quickly as it was and the damage which occurred was, relatively speaking, limited in its nature.
"While the incident was unexpected and definitely most undesirable, it has demonstrated the genuine cohesiveness, camaraderie and spirit of co-operation that exists within the F1 paddock.
"The astonishing response from the teams and other paddock personnel was immediate, unconditional and overwhelming."
Members of the Caterham, Force India, Toro Rosso and Marussia teams, as well as other people working in the area at the time, helped clear the Williams garage in the immediate aftermath of the fire.
McLaren have offered Williams any help required - such as a loan of equipment - to help repair facilities and prepare for the Monaco meeting in Monte Carlo, which begins on 25 May.