The Spain striker was back with his team-mates on Monday after twice being hospitalised last week with kidney stones.
But his illness means that the Champions League encounter has come too soon.
Villa will not travel to Italy, instead remaining in Spain to work on his fitness.
“Today I returned to train with my team-mates, but after the colic of last week I am still not 100%," he posted on Twitter.
"So we have decided to stay in Barcelona and train hard these two days! Thank you to everyone!"
Villa has only played 16 league games this season for the Catalan giants, scoring just six goals.