The car had been in the Circuit de Catalunya garage when the fire broke out as the team posed for a victory photograph following Pastor Maldonado's first Formula One win eight days ago.
Photographs showed it surrounded by charred debris and covered by extinguisher foam but a team spokeswoman said the chassis was fine.
Williams' chief operations engineer Mark Gillan said in a team preview that while preparations for Monaco had been "somewhat hampered" by the fire, the team was ready to go racing.
"The impact of the fire has been mitigated by what can only be described as a Herculean effort by the factory and our suppliers to restock both the damaged equipment and car parts," he said.
"We would also like to thank the generous offers of help from the other teams, highlighting once more the excellent sportsmanship that exists in Formula One and high levels of comradery throughout the pit lane."
Maldonado's win, from pole, in Barcelona was the first for Williams in nearly eight years and made him the fifth different winner in five races this season.
Both the Venezuelan and Senna have strong records on Monaco's tight and twisty streets in the junior GP2 series and will be aiming for another solid points finish in the season's glamour race.
"I am full of confidence after my win at the last race so I go to Monaco with high hopes of getting another strong result for the team," said Maldonado.