The film's team was present at the San Diego Comic-Con and after it took to the stage, Abrams said "something was missing", according to The Hollywood Reporter.
"There is something missing tonight. There is someone missing tonight," said producer Abrams, standing alongside stars Chris Pine, Zachary Quinto and Zoe Saldana.
Yelchin played Chekov in three of the films in the rebooted franchise.
"As wonderful as this is to be here with all of you and to be celebrating the 50th anniversary of Star Trek, there is something wrong tonight," said Abrams, who directed Yelchin in the first two Star Trek films, released in 2009 and 2013, and produced Beyond.
"Anton Yelchin should be here," Abrams continued. "Anton's parents are here - Irina and Victor. We love their son, and if I could ask everyone to have a moment of silence for our dear friend Anton."
Following the moment of silence, the San Diego Symphony began to play a medley of Star Trek theme music. During the performance, a light show appeared above the audience's heads while fireworks exploded over the marina.
Quinto, who plays Spock in the series, also said a few words for the late Leonard Nimoy, who died earlier this year.
"Beyond" sees the crew of the USS Enterprise separated following an attack lead by the the dictator Krall (Elba) that leaves them stranded in a hostile, mysterious world. The movie hits the US theatres today.
