Having originally named just one outside-half in his Six Nations squad after ignoring the likes of Fredric Michalak, France coach Marc Lievremont was dealt a severe blow when Beauxis injured his back playing club rugby for Stade Francais last weekend.
Beauxis' injury persuaded Lievremont to call up Francois Trinh-Duc, who had then been expected to start the round three match against the reigning Six Nations champions at the Stade de France.
Instead, Lievremont has decided to move Baby closer to the pack as he opts for an inexperienced half-back combination following the decision to play youngster Morgan Parra at No9.
"We regret the withdrawal of Lionel Beauxis," said Lievremont.
"Events therefore dictate our choice. We know it's not ideal. We need our best team against Wales. Francois only arrived on Monday.
"We think he (Baby) has all the qualities to play in that position even if he rarely plays there for his club. We have confidence in Benoit Baby."
Despite having only goal kicked for his country on one occasion, Bourgoin's Parra will take over the kicking duties against Warren Gatland's tournament favourites.
Lievremont makes five changes in total from the side that beat Scotland in their last championship outing.
In the backs, Maxime Medard reverts to full-back in place of Toulouse team-mate Clement Poitrenaud, Julien Malzieu is recalled to the wing and uncapped Stade Francais centre Mathieu Bastareaud comes straight into the starting line up after receiving a late call up to the squad.
"We had to choose (who to call up) between Mathieu Bastareaud and Damien Traille, but Traille is ill and only played an hour (at the weekend) while Florian Fritz is still suspended," explained Lievremont.
"Mathieu has the profile to come into this team and bring his determination and power. He has played well for Stade."
Sale's Sebastien Chabal takes over from Romain Millo-Chluski in the second row, while Sylvain Marconnet will equal Christian Califano's record of 72 French caps for a prop forward having been called up following injuries to Nicolas Mas and Benoit Lecouls.
Maxime Medard (Toulouse); Julien Malzieu (Clermont-Auvergne), Mathieu Bastareaud (Stade Francais), Yannick Jauzion, Cedric Heymans (both Toulouse); Benoit Baby (Clermont-Auvergne), Morgan Parra (Bourgoin); Fabien Barcella (Biarritz), Dimitri Szarzewski, Sylvain Marconnet (both Stade Francais), Lionel Nallet (Castres, captain), Sebastien Chabal (Sale), Thierry Dusautoir (Toulouse), Fulgence Ouedraogo (Montpellier), Imanol Harinordoquy (Biarritz)
Replacements: Benjamin Kayser (Leicester), Thomas Domingo (Clermont-Auvergne), Romain Millo-Chluski (Toulouse), Louis Picamoles (Montpellier), Sebastien Tillous-Borde (Castres), Francois Trinh-Duc (Montpellier), Clement Poitrenaud (Toulouse)