Nimoy, who played Mr. Spock to Shatner's Captain Kirk on the long-running TV show and in movies, died Friday at the age of 83.
His son Adam told the Associated Press that he died of end-stage chronic obstructive pulmonary disease.
The actor revealed he was struggling with the ailment in 2014, according to the New York Times. Nimoy had been a smoker, which contributed to the ailment, before he gave up the habit years ago.
Shatner tweeted today that he was unable to get back to California in time for the funeral because he was in Florida doing a benefit for the Red Cross.
I feel really awful. Here I am doing charity work and one of my dearest friends is being buried.— William Shatner (@WilliamShatner) February 28, 2015
"I loved him like a brother," Shatner wrote on Facebook. "We will all miss his humor, his talent, and his capacity to love."
Though he was best known for playing Spock in "Star Trek," Nimoy also worked in the theater, portraying Tevye in "Fiddler on the Roof," and published poetry and books of photography.