The striker fractured the shinbone in his left leg during Barca's 4-0 FIFA Club World Cup semi-final victory over Al-Sadd on Thursday and will undergo surgery on Monday.
Barca midfielder Cesc Fabregas has revealed his team-mates are desperate to win Sunday's final against Santos in Yokohama to help boost Villa's spirits while FIFA have given the Catalans the all-clear for their players to wear t-shirts supporting the injured forward.
Villa showed his appreciation for the show of support by the team and his fans on his Facebook page.
"Hello friends! I'm moved by all the messages you have sent me! Thank you so much! Don't worry, I've rested well tonight and I'm feeling a lot better," he said.
"I'm happy that I'm back home with my family. And, furthermore, I know I'm in good hands. I want to thank Doctor Pruna and, above all, Manel Estiarte. Without them, I don't know what I would have done on the journey home!
"Now there's less time to wait for me to recover! More to come."
The 30-year-old is Spain's all-time record scorer and is in a race against time to be fit for Euro 2012.