Getafe sports chief Robert Planas was angry with Barcelona counterpart Robert Fernandez after Saturday's defeat.
Robert was critical of the Getafe pitch at the final whistle, with the belief it contributed to Ousmane Dembele's thigh injury.
Barca coach Ernesto Valverde also mentioned the turf in his post-match media conference.
Cadena SER says Planas, after hearing Robert's comments on TV, made a beeline for the Barca chief to remonstrate.
Witnesses say the conversation became heated, with Planas making it clear to Robert that his comments were out of order.