The stoppage came in the 22nd minute with the Uruguayan removing the injured bird from the pitch after it had apparently been hit by the ball.
Speaking about the incident, Spanish media reported Gimenez as saying: "I asked the referee what was happening. He told me it was because of the pigeon and I said: 'Seriously? You stopped the match because of the pigeon?'
"I picked it up. I don't know if there's supposed to be a protocol. I hope it wasn't seriously hurt."
It was Gimenez's second assist of the match after setting up Atletico's opener, flicking on a long throw for Alexander Sorloth to score in the fifth minute.
Carlos Soler then responded for the visitors four minutes later.
Nicolas Gonzalez then scored twice either side of a Mikel Oyarzabal strike as Diego Simeone's side strengthened their hold on third place in the league.
