Footage of the moment has been shared on Twitter and viewed 2.3million times.
Bullfighting fans considered the gesture as a sign of respect for the animal - but commenters on social media and animal rights groups have slammed the incident.
Silvia Barquero Nogales, leader of Spain's Animalist Party Against Mistreatment of Animals (Pacma) political party, told the Daily Mail: 'Only a malicious and perverse mind could torture an animal until the blood pours down its legs and then wipe its face with a tissue.
'The matador is just disguising for his lack of empathy. Abolish bullfighting now!'
Meanwhile, others commented online calling the matador 'sadistic', 'psychopathic' and 'hypocritical' as he went on to kill the bull moments later.
However, bullfighting fans said that de la Puebla was showing respect to the animal as other famous matadors have done in the past, such as Jose Gomez Ortega.
Land-based animals have the ability to produce tears to lubricate their eyes, although it is widely believed that only humans produce emotional tears.