The sketch series also paid tribute to the late comedian by sharing The Java Junkie, a short film that he starred in, on Twitter.
No further details about his death have been revealed.
Like his brother, Peter began his career in the Second City comedy troupe, before joining SNL in 1979. He worked on the late-night series as both a writer and a cast member for one year, and earned an Emmy nomination for outstanding writing in a variety or music program during that time.
Peter and Dan worked together in the years that followed, in flicks including Coneheads, Spies Like Us and Dragnet. The Aykroyd brothers also co-wrote the 1991 comedy Nothing but Trouble.