Murray has only made four appearances since Fenlon arrived at the club in November after being troubled by a hip injury, and was not in the squad for the William Hill Scottish Cup final defeat by Hearts after making his comeback the previous weekend.
The 31-year-old, who made more than 300 appearances for Hibs either side of spells with Rangers and Norwich, had been expecting the news.
He told the club's official website: "I want to thank everyone for their support, especially this season with my testimonial. I've obviously loved my time at Hibernian.
"To be fair to the gaffer, things have moved on and changed since he's come in so there's no real surprise for me.
"I'm looking forward to my next challenge and wish all the Hibernian supporters all the best for next season."