Thursday's statement about Alves' injury would have worried Brazil supporters with the veteran right-back still in contention for a World Cup spot.
However, the 39-year-old moved to reassure fans on social media that he has not picked up a serious knock and explained why he did not travel to Juarez for Friday's game.
"I think the person who wrote this [Puma's statement] was not aware of the real situation... In training, on the eve of the trip, my friend Diogo, a Brazilian who plays with me, ended up hitting me on the last play of training," Alves wrote on his social media account.
"As a precaution, we decided not to travel for the last game, as there is nothing else at stake. We have big goals to fight for, and in the end, I made this decision not to travel. But thank the good God, everything is fine, everything is calm."
Pumas rectified the mistake and tweeted: "To clarify the misunderstanding regarding the injury of our player Dani Alves, Pumas wishes to state that the player received a knock on his knee at the end of training and as a precaution, did not travel to face Juarez.
- Notebook: The inside stories from world football
"The injury requires basic treatment and rest. Due to a lack of communication and the trip to Ciudad Juarez, erroneous information was published. For that mistake, we apologise to Dani Alves."
Alves joined Pumas in July after his contract with Barcelona expired and has made 12 appearances for the Mexican side.
"Not only am I enthusiastic but I'm working for it," Alves said last week. "My goal is to go to the World Cup in Qatar. I prepare and work every day for it. I've already said it. I have a history with the national team, 16 years and all that I have achieved, gives me credit to go to the World Cup."