The Spanish football federation classes the removal of a shirt to display any form of publicity, slogan or picture as a serious offence punishable with a fine of between 2,000 euros and 3,000 euros.
Spain's all-time top scorer came on as a late substitute when Barca beat Real Sociedad 5-1 in their La Liga opener on Sunday and netted near the end after an eight-month layoff with a broken leg.
The 30-year-old ripped off his shirt in the celebration to reveal a photo of his wife and two daughters underneath the slogan "Impossible without you," and was shown a yellow card by the referee.
Villa broke his leg at the Club World Cup last December, missing the national team's Euro 2012 triumph as he continued his recovery. His return on Sunday in the 74th minute received a huge Nou Camp ovation.
"It has been a difficult time and it is nice to be back," Villa said after the match.
"I am pleased to be able to say I can forget about the injury now. I have had five weeks training at the maximum level but my body still struggles to reach the levels required to play 90 minutes. I'll keep on working until I van eventually play a full game again.
"Because of me, I am sure it has been a difficult time for (my family) as well."